Speaker Mike Johnson had been pressing to issue the invitation for weeks, seeking to hug Mr. Netanyahu closer as some Democrats, particularly progressives, repudiate him and condemn his tactics in the war, which have caused tens of thousands of civilian casualties in Gaza and a humanitarian disaster for Palestinians.

Republicans have unequivocally backed Mr. Netanyahu’s policies, while Democrats, many of whom view his far-right government as an impediment to peace, have been deeply split over them. On Friday, Mr. Biden called for a permanent cease-fire and said, “It’s time for this war to end.”

Senator Chuck Schumer of New York, Democrat of New York and the majority leader, earlier this year called for Mr. Netanyahu to step down and for new elections. In response, Mr. Netanyahu assailed Mr. Schumer in a closed-door virtual speech to Senate Republicans. Mr. Schumer at the time had refused to allow Mr. Netanyahu to make a similar address to Senate Democrats, arguing that it was not helpful to Israel for the prime minister to address American lawmakers in a partisan fashion.

Even before the invitation went out on Friday afternoon, the prospect of Mr. Netanyahu’s visit to the Capitol had divided Democrats. Senator Bernie Sanders of Vermont said he would boycott a speech from the prime minister, and House progressives said they would plan some sort of gesture to register their opposition to Mr. Netanyahu’s government and to his presence at the Capitol.

Former Speaker Nancy Pelosi had said Mr. Schumer should not add his name to the invitation.

But on Friday, Mr. Schumer, along with Representative Hakeem Jeffries of New York, the House Democratic leader, and Senator Mitch McConnell of Kentucky, the minority leader, and Mr. Johnson, extended a bipartisan invitation for Mr. Netanyahu to address all of Congress at once in a formal joint meeting of both chambers.

“The existential challenges we face, including the growing partnership between Iran, Russia and China, threaten the security, peace and prosperity of our countries and of free people around the world,” the four leaders wrote in the letter. “To build on our enduring relationship and to highlight America’s solidarity with Israel, we invite you to share the Israeli government’s vision for defending democracy, combating terror and establishing a just and lasting peace in the region.”

The lack of a date was somewhat unusual for an invitation to a foreign leader.

Mr. Netanyahu last addressed Congress in 2015, during a more formal joint meeting in which he took the podium before members of the House and Senate to argue strenuously against the policies of President Barack Obama related to a nuclear agreement with Iran. At the time, 58 members of Congress boycotted the speech.

The latest invitation is part of a weekslong campaign that House Republicans have undertaken to spotlight Democratic divisions on Israel, while portraying their own party as stalwart friends of the Jewish state.

Progressive groups called the move disgraceful. In a statement, Eva Borgwardt, a spokeswoman for IfNotNow, a left-wing Jewish group that has protested the war, said all four congressional leaders “will forever be remembered as the leaders who invited the war criminal Benjamin Netanyahu to give a speech to Congress in the middle of Israel’s genocidal assault on Gaza, days after he crossed President Biden’s red line on an invasion of Rafah.”