Republican allies of Donald J. Trump are calling for revenge prosecutions and other retaliatory measures against Democrats in response to his felony conviction in New York.

Within hours of a jury finding Mr. Trump guilty last week, the anger congealed into demands for action. Since then, prominent G.O.P. leaders in and out of government have demanded that elected Republicans use every available instrument of power against Democrats, including targeted investigations and prosecutions.

The intensity of anger and open desire for using the criminal justice system against Democrats after the verdict surpasses anything seen before in Mr. Trump’s tumultuous years in national politics. What is different now is the range of Republicans who are saying retaliation is necessary and who are no longer cloaking their intent with euphemisms.

Stephen Miller, a former senior adviser to Mr. Trump who still helps guide his thinking on policy, blared out a directive on Fox News after a jury found Mr. Trump guilty of falsifying financial records to cover up a 2016 campaign hush-money payment to a porn actress. Mr. Miller posed a series of questions to Republicans at every level, including local district attorneys.

“Is every House committee controlled by Republicans using its subpoena power in every way it needs to right now?” he demanded. “Is every Republican D.A. starting every investigation they need to right now?”

“Every facet of Republican Party politics and power has to be used right now to go toe-to-toe with Marxism and beat these Communists,” Mr. Miller said, using the catchall slurs Trump allies routinely use against Democrats.

Stephen K. Bannon, the former chief strategist to Mr. Trump, said in a text message to The New York Times on Tuesday that now was the moment for obscure Republican prosecutors around the country to make a name for themselves by prosecuting Democrats.

“There are dozens of ambitious backbencher state attorneys general and district attorneys who need to ‘seize the day’ and own this moment in history,” Mr. Bannon wrote.

And Senator Marco Rubio of Florida, the top Republican on the Senate Intelligence Committee who is in contention to be Mr. Trump’s running mate, wrote on X that President Biden was “a demented man propped up by wicked & deranged people” and it was now time to “fight fire with fire” — using flame emojis to represent the fire.

Officials with the Trump campaign did not respond to requests for comment.

Seeking retribution through the justice system is hardly a new concept for Mr. Trump. In 2016, he echoed and encouraged chants of “lock her up” against his opponent, Hillary Clinton, whom the authorities had declined to prosecute for using a private email server while she was secretary of state.

While president, Mr. Trump repeatedly told aides he wanted the Justice Department to indict his political enemies. The Justice Department opened various investigations of Mr. Trump’s adversaries but did not ultimately bring charges — infuriating Mr. Trump and contributing to a split in 2020 with his attorney general, William P. Barr. Last year, Mr. Trump promised that if elected again, he would appoint a “real special prosecutor” to “go after” Mr. Biden and his family.

Now, it remains unclear whether calls for legal retribution will amount to much in the way of actual prosecutions, at least in the short term. Without control of the White House, people close to Mr. Trump are urging district attorneys and attorneys general in red states to start aggressively targeting Democrats for unspecified crimes.

A central tenet of their argument is that the four criminal cases in four different jurisdictions against Mr. Trump are illegitimate and nothing more than political weaponization of the justice system. They continue to put forward the theory, without evidence, that all four cases are the result of a conspiracy by Mr. Biden — implicitly or explicitly rejecting the notion that Mr. Trump has been charged with crimes based on evidence.

But based on their premise that the charges — and now convictions in the fraudulent business records case — are baseless and were invented for political reasons, they are arguing that Republican prosecutors not only should but can do the same thing to Democrats. In short, having accused Democrats of “lawfare” — or using the law to wage war against political opponents — Republicans are saying they should respond in kind.

Some veteran Republican lawyers have sought to dress up the need for such retribution as a matter of constitutional principle. Among those calling for eye-for-an-eye prosecutions is John C. Yoo, a University of California, Berkeley, law professor best known as the author of once-secret Bush administration legal memos declaring that the president can lawfully violate legal limits on torturing detainees and wiretapping without warrants.

“In order to prevent the case against Trump from assuming a permanent place in the American political system, Republicans will have to bring charges against Democratic officers, even presidents,” Professor Yoo wrote in an essay published by The National Review.

He added: “Only retaliation in kind can produce the deterrence necessary to enforce a political version of mutual assured destruction; without the threat of prosecution of their own leaders, Democrats will continue to charge future Republican presidents without restraint.”

Mr. Trump’s closest allies on Capitol Hill are less bothered about finding a high-minded constitutional rationale.

“President Biden should just be ready because on Jan. 20 of next year when he’s former President Joe Biden, what’s good for the goose is good for the gander,” said Representative Ronny Jackson, a Texas Republican and close Trump ally, in an appearance on the pro-Trump network Newsmax.

Mr. Jackson said: “I am going to encourage all of my colleagues and everybody that I have any influence over as a member of Congress to aggressively go after the president and his entire family, his entire crime family, for all of the misdeeds that are out there right now related to this family.”

Some of the rhetoric has gone even further.

“Not just jail, they should get the death penalty,” said Laura Loomer, a far-right and anti-Muslim activist with a history of expressing bigoted views, in a podcast appearance after the verdict. Ms. Loomer, a onetime Republican nominee for a House seat in Florida, is not officially part of the Trump campaign. Mr. Trump, however, has praised her as “very special,” invited her to travel with him on his private plane and has met with her at his private clubs.

On social media, there has been an explosion of violent rhetoric and threats against the judge in the New York criminal case, Juan M. Merchan, and the Manhattan district attorney, Alvin L. Bragg, who brought the charges against Mr. Trump.

Representative Jim Jordan of Ohio, a close Trump ally who is chairman of the House Judiciary Committee, sent a letter this week demanding testimony by Mr. Bragg and one of his top trial lawyers in the case, Matthew Colangelo.

Mr. Bragg’s office has not yet responded to the letter, but the demand appears to set the stage for an eventual subpoena and court fight. After the indictment last year, Mr. Jordan subpoenaed a former prosecutor in Mr. Bragg’s office, Mark Pomerantz, who eventually sat for a deposition about the investigation.

Mr. Jordan this week also proposed barring federal law enforcement grants from going to Mr. Bragg’s office and to the office of the district attorney in Fulton County, Ga., where Mr. Trump is facing state charges over attempted subversion of the 2020 election.

Speaker Mike Johnson went on Fox News and called on the Supreme Court to “step in” and overturn the Manhattan conviction, granting Mr. Trump immunity from prosecution. In the Senate, a group of Trump allies signed a letter declaring that they will oppose major legislation and Biden administration nominees, although they tend not to vote for Biden policies and nominees anyway.

But the more extreme calls for not just oversight scrutiny and political obstructionism but revenge prosecutions are coming from former senior Trump administration officials and people close to the former president who are expected to play even larger roles in a potential second term. Their message is often apocalyptic.

There is no longer any room, they argue, for weaklings who fetishize decency and restraint.

Mike Davis, a former top Senate Judiciary Committee lawyer who is a close associate of Mr. Trump, is calling for an investigation of the investigators, similar to how the Justice Department under Mr. Trump used the special counsel investigation led by John Durham in a yearslong, unsuccessful attempt to find a basis to accuse high-level Obama administration officials of a crime because of the Russia investigation.

“The Republican attorneys general in Georgia and Florida and the county attorney in Maricopa County, Ariz., need to open investigations” into the prosecutors and investigators pursuing the indictments of Mr. Trump and his allies, Mr. Davis said. He added, “Then on Day 1, when he wins, President Trump needs to open a criminal civil rights investigation.”

Jeff Clark, a former Trump Justice Department official who has been indicted in the Georgia election case for his role in helping Mr. Trump’s attempt to overturn the 2020 vote in that state, has offered another suggestion. He has called for “brave” district attorneys in conservative areas to file lawsuits in federal court against people involved in criminal cases against Mr. Trump, under federal laws that allow people to seek monetary damages from government officials who violate their constitutional rights.

His theory is that the cases are a conspiracy to prevent Mr. Trump from effectively running for president. It remains unclear, however, why local criminal prosecutors would have legal standing to go into federal court and bring such lawsuits. A spokeswoman for Mr. Clark’s employer, the Center for Renewing America, a pro-Trump think tank, did not respond to a request for comment.

But there is no room on this issue for moderate or traditional Republicans, such as Larry Hogan, a former governor of Maryland and a star G.O.P. recruit to run for the Senate in the blue state. Mr. Hogan erred unforgivably in the eyes of the Trump team when he implored Americans “to respect the verdict and the legal process” regardless of the outcome.

Chris LaCivita, a top Trump adviser, addressed Mr. Hogan in a post on X: “You just ended your campaign.” And even though a victory by Mr. Hogan could make the difference between whether Republicans or Democrats control the Senate next year, Mr. Trump’s daughter-in-law Lara Trump, who is also the co-chair of the Republican National Committee, said on CNN that Mr. Hogan “doesn’t deserve the respect of anyone in the Republican Party.”