A Republican invitation for Israel’s prime minister, Benjamin Netanyahu, to address Congress next month is highlighting the tensions between President Obama and Mr. Netanyahu and has kicked off a bizarre diplomatic race over who will be the first to lay out a new proposal to reopen the stalled Israeli-Palestinian peace talks.

For three months, White House officials have been debating whether the time has come for Mr. Obama to make a major address on the region’s turmoil, including the upheaval in the Arab world, and whether he should use the occasion to propose a new plan for peace between Israelis and Palestinians.

One administration official said that course was backed by Secretary of State Hillary Rodham Clinton and the president himself, but opposed by Dennis B. Ross, the president’s senior adviser on the Middle East.

As the administration has been pondering, Mr. Netanyahu, fearful that his country would lose ground with any Obama administration plan, has been considering whether to pre-empt the White House with a proposal of his own, before a friendly United States Congress, according to American officials and diplomats from the region.

“People seem to think that whoever goes first gets the upper hand,” said Daniel Levy, a former Israeli peace negotiator and a director at the New America Foundation. Using Mr. Netanyahu’s nickname, he said: “If Bibi went first and didn’t lay out a bold peace plan, it would be harder for Obama to say, actually, despite what you said to Congress and their applause, this is what I think you should do.”

The political gamesmanship between the two men illustrates how the calculation in the Middle East has changed for a variety of reasons, including the political upheaval in the Arab world. But it also shows the lack of trust and what some officials say is personal animosity between Mr. Obama and Mr. Netanyahu.

White House officials are working on drafts of a possible proposal, but they have not decided how detailed it will be, or even whether the president will deliver it in a planned speech. If Mr. Obama does put forward an American plan, officials say it could include four principles, or terms of reference, built around the final status issues that have bedeviled peace negotiators since 1979.

The terms of reference could call for Israel to accept a Palestinian state based on the 1967 borders. For their part, Palestinians would have to accept that they would not get the right of return to land in Israel from which they fled or were forced to flee. Jerusalem would be the capital of both states, and Israeli security would have to be protected.

Mr. Netanyahu has made it clear that he wants Israel’s security needs addressed before any peace deal with the Palestinians. He has become even more concerned about security because shifts in power among Arab states in recent months have weakened Israel’s already fragile relations with its neighbors, particularly Egypt.

The tussling between the Obama administration and the Israeli government reached a peak last week when Mrs. Clinton, in Washington at a meeting of the U.S.-Islamic World Forum, announced that Mr. Obama would be “speaking in greater detail about America’s policy in the Middle East and North Africa in the coming weeks.”

Her announcement electrified Israeli officials, who quickly got on the phone with American officials and journalists to determine whether Mr. Obama had decided to put an American plan on the table. He had not made such a decision, and White House officials cautioned that the internal debate was still going on.

But two days later, the House speaker, John A. Boehner of Ohio, announced his intention to invite Mr. Netanyahu to address a joint meeting of Congress. “America and Israel are the closest of friends and allies, and we look forward to hearing the prime minister’s views on how we can continue working together for peace, freedom and stability,” Mr. Boehner said in a news release.

Like many other foreign leaders, Mr. Netanyahu has addressed Congress before. He did so in 1996, and four other Israeli prime ministers have over the past 35 years. The platform gives American elected leaders the opportunity to publicly demonstrate their support for Israel before the politically crucial Israel lobby.

Mr. Netanyahu’s address will coincide with the planned meeting of the American Israel Public Affairs Committee, arguably the most powerful of the American groups that advocate for Israel.

Brendan Buck, Mr. Boehner’s press secretary, said that staff members had received no pushback from the White House about the invitation to Mr. Netanyahu. “Obviously, it’s a troubled time for the region,” he said. “Our members have been very interested in demonstrating that we stand with Israel.”

Last November, Representative Eric Cantor, Republican of Virginia, told Mr. Netanyahu that the new G.O.P. majority in the House would “serve as a check on the administration,” in a statement that was rare for its blunt disagreement on American foreign policy as conveyed to a foreign leader.

Mr. Cantor put out a statement after a meeting with Mr. Netanyahu saying that he “made clear that the Republican majority understands the special relationship between Israel and the United States, and that the security of each nation is reliant upon the other.”

Brian Katulis, a national security expert with the Center for American Progress, a liberal research organization, said that Republicans were trying to “make Israel a partisan wedge issue.”

“And that’s bad for Israel, and that’s bad for the United States,” Mr. Katulis said. But he added that the administration would never publicly, or even privately, oppose the notion of an Israeli leader addressing Congress.

Two American officials, speaking on condition of anonymity out of diplomatic caution, said they thought that if Mr. Netanyahu intended to make a bold proposal for a peace deal with the Palestinians, he would do so before his own people in the Knesset.

“Instead of focusing on peace-making, everybody seems to be focused on speech-making,” said Martin S. Indyk, vice president for foreign policy at the Brookings Institution and a former United States ambassador to Israel. “And unless the speeches generate peace negotiations, making speeches will not generate peace.”

Much of the debate is taking place under a pending deadline of the United Nations General Assembly meeting scheduled in September, when the Assembly is expected to broadly endorse Palestinian statehood in a vote that could prove deeply embarrassing to Israel and the United States, which are both expected to vote against it.