Former President Donald J. Trump out-raised President Biden for the second consecutive month in May, outpacing his successor by roughly $81 million in donations over the last two months as he rode a surge of financial support after his felony conviction.

In May, Mr. Biden’s campaign and its joint operation with the Democratic National Committee raised $85 million, compared with $141 million for Mr. Trump and the Republican National Committee, according to the two campaigns. In April, the Trump team also brought in $25 million more than the Biden team.

The Biden campaign said it entered June with $212 million on hand combined with the party. The Trump operation and R.N.C. have not released a full tally of their cash on hand since the end of March. A partial count on Thursday, revealed in Federal Election Commission filings, showed that Mr. Trump had amassed a war chest of at least $170 million with the party.

Overall, Mr. Trump was a daunting $100 million behind Mr. Biden at the start of April. In two months, he cut that cash deficit by at least half. And for the first time, Mr. Trump’s principal campaign committee had more cash than Mr. Biden’s: $116.5 million to $91.6 million.

The full accounting of both sides’ finances will be made public in federal filings next month. But the combination of Mr. Trump’s improved fund-raising and Mr. Biden’s heavier spending on advertising this spring appears to put the two sides on a path to enter the summer relatively close to financial parity.

“Yes, Trump is raising a lot more money now, and that should scare people,” said Brian Derrick, a strategist who founded a Democratic fund-raising platform called Oath. “But at the end of the day, Biden has the funds that he needs to run a really strong campaign.”

Mr. Trump has narrowed the gap by bringing in a deluge of online donations after his criminal conviction in New York on May 30. In the minutes after the verdict, guilty on 34 felony counts, contributions came in so fast that they briefly overwhelmed the Republican Party’s online donation portal, WinRed.

The Trump campaign has said it raised $53 million online in the first 24 hours and $70 million in the first 48 hours after the verdict. The conviction uncorked a gusher of mega-donations, too, including a $50 million contribution from the reclusive billionaire Timothy Mellon to a pro-Trump super PAC the day after the verdict.

At the conclusion of the Republican primary race, the Biden campaign and its allies had argued that for all of the president’s electoral vulnerabilities — nagging inflation, poor approval ratings, lingering concerns about his age — one clear advantage would be cash.

Even if that edge has since evaporated, the Biden campaign says it used its early financial lead to build out a political infrastructure in battleground states that will pay dividends in November. On Thursday, the campaign announced that it had hired its 1,000th staff member across 200 offices in those states.

“What’s in his F.E.C. report does not translate to boots on the ground tomorrow,” Dan Kanninen, Mr. Biden’s battleground states director, said in an interview. “That was built over time that Donald Trump cannot get back.”

Steven Cheung, Mr. Trump’s communications director, said that Mr. Biden had wasted money on ineffective television advertising.

“President Trump’s record-breaking fund-raising numbers prove Crooked Joe Biden’s witch hunts against President Trump, skyrocketing inflation, and the illegal border invasion have united the American people around the fact that another four years of Biden will mean the end of our country,” Mr. Cheung said.

Money alone is rarely determinative in big races, like for the presidency, because voters are already well-informed about the candidates. But some of the most important voters this year appear to be those who have tuned out — and breaking through to them can cost considerable money.

For months, Mr. Trump and his allies simply did not have the money to reach these voters. While his path to the Republican nomination was hardly bruising, he emerged from the primary race in relatively poor financial shape compared with Mr. Biden’s operation, which had been squirreling away money for nearly a year.

Mr. Biden had consolidated his party’s biggest donors. Mr. Trump had not done so on his side.

But that slow start also gave Mr. Trump much more room to grow. In the weeks after he dispatched Nikki Haley, his final Republican rival, Trump bundlers described an almost furtive effort to get back into his good graces.

A fund-raising dinner at Mr. Trump’s Florida estate, Mar-a-Lago, in mid-February, a few weeks before Ms. Haley’s exit, served as an important inflection point as Trump fund-raisers signaled to wavering donors that the time for indecision was coming to a close. A fund-raising dinner hosted by John Paulson, a hedge-fund billionaire, raised $50 million, the campaign has said. And in just the last month, well-to-do holdouts like the Blackstone co-founder Stephen A. Schwarzman have signaled that they plan to support Mr. Trump.

Wrapping up the nomination also allowed Mr. Trump to form a joint fund-raising committee with national and state Republican parties, a seemingly technical step that meant he could suddenly raise hundreds of thousands of dollars more from each donor. Mr. Biden had been raising money in those larger increments for many months.

Online contributions will be increasingly crucial going forward because the campaigns cannot tap their largest donors for repeat contributions. And Mr. Trump’s base appears to have been highly animated by his conviction. His campaign said one-quarter of the contributors in May were new.

The question for Mr. Trump is how many of those people become repeat contributors. The Biden campaign has aggressively cultivated online recurring contributors, a group that accounted for $5.5 million in April and more than that in May, though the campaign did not provide a specific figure.

So far, Mr. Biden has enjoyed a tremendous advertising advantage over Mr. Trump.

From the beginning of the year through this month, Mr. Biden’s operation had aired or reserved roughly $35.4 million in the top six battleground states. Mr. Trump’s operation had aired essentially nothing in those states, about $60,000 in ads, according to records from AdImpact, a media tracking firm.

Trump advisers say the fact that Mr. Biden has spent tens of millions of dollars in key states without altering the trajectory of the race bodes ill for the president’s chances in November.

Fund-raisers for Mr. Biden insist that they will maintain their upper hand when outside groups are accounted for. The constellation of pro-Biden super PACs and nonprofit groups outspent Trump allies by roughly 50 percent across the six most contested battlegrounds, according to AdImpact’s data.

Still, that Biden dominance of the airwaves is not likely to continue.

Mr. Trump’s main super PAC, Make America Great Again Inc., and its nonprofit arm, which can keep its donors secret, paid nearly $17 million in the first half of the year for ads in Pennsylvania, the only battleground where it made a significant investment.

But this week, MAGA Inc. began reserving nearly $30 million in airtime starting in early July in Pennsylvania and Georgia, as part of what it has said will be a $100 million summer advertising blitz. Other pro-Trump super PACs are beginning to plan advertising pushes, too.

Democratic fund-raisers for Mr. Biden said that they expected Mr. Trump to eventually catch up and had received such guidance explicitly from Rufus Gifford, the campaign’s top fund-raising official, at recent briefings. One Biden bundler compared the 2024 race to the summer of 2012, when Mitt Romney steadily chipped away at President Barack Obama’s fund-raising lead.

Other Democratic allies have been more taken aback by the recent turn of events, speculating that the lasting political impact of Mr. Trump’s conviction will not be on voters but on donors.

“It’s nerve-racking to see the money race even out,” said Jon Reinish, a Democratic political strategist. “That was supposed to be one of Biden’s real advantages. He’s also been spending money for months and that doesn’t seem to be moving the needle much in terms of polling. Hopefully that changes as we get even closer.”

For now, Mr. Biden is racing to replenish his coffers in June. He held a $30 million event in Los Angeles with Mr. Obama and Hollywood stars, as well as an $8 million backyard fund-raiser on Tuesday at the home of Terry McAuliffe, the former Virginia governor, with former President Bill Clinton among those in attendance.

Others are hoping that Biden surrogates can help raise money.

On the day of the first general-election debate next week, three leading Democratic governors — Andy Beshear of Kentucky, JB Pritzker of Illinois and Gretchen Whitmer of Michigan — will be in Los Angeles for a fund-raiser.

At the same time, a wide range of Republican vice-presidential hopefuls will headline a debate-watch party in Atlanta that will double as a fund-raiser.