WASHINGTON — It is a truism of Middle East peacemaking that the United States is the pivotal player — the most credible broker between the Israelis and the Palestinians. But with talks at a standstill, the Obama administration now finds itself on the sidelines, and Europe is emerging as the key diplomatic actor.

Prime Minister Benjamin Netanyahu of Israel and the Palestinian president, Mahmoud Abbas, have crisscrossed the Continent in recent weeks, trying to woo leaders who are weighing whether to support a Palestinian bid for statehood at the United Nations in September. Neither man has visited Washington since the spring.

That may suit the administration just fine. The White House, several officials said, has deliberately kept a low profile since President Obama’s speech on the Middle East in May, in which he tried unsuccessfully to break the stalemate by proposing a starting point for negotiating the contours of a Palestinian state.

Europe’s rising role stems not only from American fatigue with a seemingly intractable problem, but also from the peculiar dynamics of the Palestinian campaign at the United Nations. With more than 100 countries, most in the developing world, expected to support Palestinian recognition — and the United States almost certain to oppose it — Britain, France and Germany are viewed as influential swing votes.

“Rarely has Europe been so courted when it comes to Middle East diplomacy,” said David Makovsky, a senior fellow at the Washington Institute for Near East Policy. “Europe is the prize this summer.”

For the Europeans, who have also taken a lead role in the NATO military campaign in Libya, the chance to play Middle East power broker is gratifying. But it comes with a risk, said Martin S. Indyk, director of foreign policy at the Brookings Institution and a former American ambassador to Israel. “The action in the United Nations is a bigger problem for them than for us,” he said. “It has the potential of splitting the E.U., with some siding with us and Israel and some siding with the Palestinians.”

A rift is the last thing the European Union needs, at a time when the bloc is being strained by the debt crisis in Greece. Already, the major countries appear divided, with Germany and Italy rejecting the Palestinian campaign, France and Spain receptive, and Britain on the fence.

For some Europeans, leaving the door open to Palestinian recognition is a handy way to pressure Israel to return to negotiations, which have been on ice since last fall. To break that deadlock, Mr. Obama proposed using the prevailing borders before the 1967 Arab-Israeli war, adjusted to account for Jewish settlements in the West Bank, as the basis for negotiating a new Palestinian state. Mr. Netanyahu initially rejected that formula, saying it would render Israel indefensible. But an Israeli official said that in recent weeks, Mr. Netanyahu had moved much closer to accepting the idea, provided that the Palestinians agreed to recognition of Israel as a Jewish state, something they have long refused.

Last week, the United States tried to build support for such a quid pro quo from the Quartet, a Middle East peacemaking group that also includes the European Union, the United Nations and Russia. Winning the Quartet’s endorsement would have put pressure on both sides to resume negotiations and taken much of the steam out of the Palestinian march to the United Nations.

While European countries have publicly backed Mr. Obama’s proposal for restarting the talks, several of them, as well as Russia, balked at the Jewish-state provision, officials briefed on the meeting said. Rather than issue an anodyne statement, as it often does, the Quartet chose to say nothing at all.

The Palestinian date with the United Nations looms large, though no one is exactly sure what will happen after it. Israel’s defense minister, Ehud Barak, warned that his country faced a “diplomatic tsunami.” Others worry that it will kick off a third intifada, given the political ferment elsewhere in the region.

“The conditions for massive public reaction are ripe,” Ghaith al-Omari, the executive director of the American Task Force on Palestine, said. “If things go down that path, it would be highly destabilizing.”

The United States continues to work on European allies and the Palestinians to point out the downsides of going for recognition, including the threat that Congress could vote to cut off aid to the Palestinian Authority.

Still, the administration has opted for what one Middle East diplomat called a “tactical withdrawal,” leaving it to Tony Blair, the former British prime minister who is the special envoy to the Quartet, to try to close the gaps. While the United States does not want to be isolated by vetoing a Palestinian resolution, which Mr. Obama has signaled he will do, the administration appears less agitated by this prospect than it was a few months ago.

“The U.S. is frustrated, but ultimately an outcome where it vetoes a resolution is not the end of the world,” said Robert Malley, the Middle East and North Africa program director at the International Crisis Group.

Palestinian leaders insist they are determined to go through with the drive for recognition, but it could take less aggressive forms: petitioning the General Assembly, rather than the Security Council, for nonmember status, thus sidestepping an American veto. The Palestinians could even propose a resolution that echoes Mr. Obama’s formula for talks. This is where Europe plays an important role. Without support from big countries like Britain and France, the Palestinians may opt to hold off or pursue a softer resolution. And if they go ahead at the Security Council, the Europeans could introduce an alternative resolution embracing Mr. Obama’s principles.

“The United States has put its cards on the table, but Europe has not yet done that,” said Robert Danin, a senior fellow at the Council on Foreign Relations who used to run the Jerusalem office of the Quartet. “The run-up to September is not about numbers. It’s about: Where does the West stand?”