WASHINGTON — President Trump will come under increasing pressure from visiting French and German leaders this week not to scrap the three-year-old nuclear agreement with Iran next month as American and European negotiators make tentative progress toward a new deal to toughen the limits on Tehran.

President Emmanuel Macron of France arrived Monday at the White House for the first state visit of Mr. Trump’s presidency, intent on using his unusual bond with the American president to try to persuade him to preserve the Iran deal, at least for now. While not as close personally to Mr. Trump, Chancellor Angela Merkel of Germany will follow on Friday to reinforce the message.

The back-to-back visits come weeks before a May 12 deadline set by Mr. Trump to “fix” the Iran agreement or walk away from it. Under the agreement, sealed in 2015 by President Barack Obama, Iran has curbed its nuclear program in exchange for relief from crippling international sanctions. But Mr. Trump and other critics have assailed it because it begins to expire after a decade and does not block Iran’s missile development or try to stop it from destabilizing the region.

In recent weeks, American and European negotiators have made progress toward side agreements that would lay out new standards for Iran to meet or risk the reimposition of sanctions by the West. Negotiators have generally reached a consensus on measures to constrain Iran’s ballistic missile program, according to people briefed on the talks, but remain divided over how to extend the restrictions of the original agreement due to lapse starting in 2025.

Most importantly, the Europeans want assurances that if side agreements are reached, the United States will stay in the deal, a hard commitment for American officials to make given Mr. Trump’s mercurial nature. But European leaders hope they can persuade him to hold off by showing enough progress in negotiations that he can claim he is making the deal better.

“I suspect that this will be a very difficult conversation,” said Wendy R. Sherman, the former top State Department official who negotiated the Iran deal for Mr. Obama. “I’m sure that Macron will say how important staying in the deal is to a strong trans-Atlantic relationship in all things, particularly security. I think Merkel will deliver the same message on Friday.”

Even so, the White House signaled Monday that Mr. Trump enters the talks with one set impression. “He thinks it’s a bad deal — that certainly has not changed,” said Sarah Huckabee Sanders, the White House press secretary.

The fate of the Iran agreement could influence the president’s forthcoming meeting with Kim Jong-un, the North Korean leader who already has a small nuclear arsenal. Whatever its flaws, American officials understand that canceling the Iran deal days or weeks before that meeting might complicate Mr. Trump’s chances of making an agreement with Mr. Kim.

Mohammad Javad Zarif, Iran’s foreign minister, implicitly made that point Monday by noting that the negotiations that led to the nuclear agreement between his country and six world powers involved give and take by all sides.

“And now the United States is saying, ‘What’s mine is mine and what’s yours is negotiable. But whatever I gave you, now I want it back,’” Mr. Zarif said in an interview with The National Interest, a Washington policy magazine. “Who would, in their right mind, deal with the U.S. anymore?”

Mr. Trump faces conflicting positions among his own advisers as he reconstitutes his national security team. John R. Bolton, his new national security adviser, has long advocated simply ending the Iran deal, while Mike Pompeo, set to become secretary of state, is open to keeping it if strong new provisions can be negotiated.

Mr. Macron arrived in Washington to a festive welcome. American and French flags flew on Pennsylvania Avenue as he and his wife, Brigitte Macron, were greeted at the White House by Mr. Trump and the first lady, Melania Trump.

Mr. Macron reached in for a hug and kissed Mr. Trump on both cheeks, French-style, a sign of their warm ties. The two couples headed inside for a few minutes and then out to the South Lawn, smiling and chatting casually as cameras recorded the moment.

Wielding shovels, the two presidents moved some dirt around where a tree was to be planted, a gift from the Macrons. The tree, a European sessile oak, came from Belleau Wood, where, during World War I, nearly 10,000 American Marines were killed or injured in battle in June 1918. From there, the two couples flew by helicopter to George Washington’s Mount Vernon estate for dinner.

The Macrons will return to the White House on Tuesday morning for a pomp-filled arrival ceremony on the South Lawn, complete with members of all five branches of the military in formal uniforms. The two presidents will hold meetings and conduct a joint news conference. In the evening, the Trumps will host their first state dinner, featuring rack of spring lamb and Carolina gold rice jambalaya cooked New Orleans style.

Mr. Trump, 71, and Mr. Macron, 40, have forged an unlikely friendship, despite their political differences over the Iran deal, international trade, climate change and other issues. But while Europeans consider Mr. Macron their envoy to Mr. Trump, he has had mixed success influencing the president. The two leaders teamed up to launch airstrikes against Syria this month in retaliation for a suspected chemical attack, but when Mr. Macron publicly said he had persuaded Mr. Trump to keep American troops in the country “for the long term,” the White House quickly disputed him.

Mr. Macron telegraphed his message on Iran by appearing on the president’s favorite network, Fox News, over the weekend.

Is the pact “a perfect thing for our relationship with Iran? No,” he said on “Fox News Sunday.” “But for nuclear, what do you have as a better option? I don’t see it. What is the what-if scenario or your Plan B? I don’t have any Plan B for nuclear against Iran.”

Mr. Macron added that he supported modifications to the deal, known as the Joint Comprehensive Plan of Action, or J.C.P.O.A. “My point is to say, don’t leave now to J.C.P.O.A. as long as you don’t have a better option for nuclear, and let’s complete it with ballistic missile and a regional containment,” Mr. Macron said.

Mr. Zarif picked up on that on Monday. “President Macron is correct in saying there’s no ‘Plan B’ on JCPOA,” Mr. Zarif wrote on Twitter. “It’s either all or nothing. European leaders should encourage President Trump not just to stay in the nuclear deal, but more importantly to begin implementing his part of the bargain in good faith.”

The negotiations with European officials, led by Brian Hook, the State Department’s director of policy planning, have found some common ground, according to people briefed on the talks. Negotiators are developing two annexes, or side agreements, to the original deal, one intended to constrain Iran’s missile program and the other to confront its aggressions in the Middle East.

Negotiators have agreed on strong measures to impose sanctions on Iran if it tests long-range missiles and are debating a framework document to respond to testing of short- and medium-range missiles. They have agreed that Iran would be sanctioned if it blocks international nuclear inspectors from any site, including military sites. And they have made progress in defining a trigger for reimposing sanctions lifted as part of the 2015 deal — if Iran were found to have expanded its nuclear program enough to allow it to develop a weapon in less than a year.

But negotiators are divided over what would happen then. The Trump administration insists that sanctions be reimposed automatically if Iran trips that one-year wire, while the Europeans want the trigger to be a determination that Iran’s expansion is inconsistent with its civilian nuclear program. If the Americans and Europeans ultimately agree, that would effectively end the expiration provisions known as “sunsets” by making the one-year limit permanent.

“The Europeans have moved very far in a few months, and I think this should be bridgeable, but of course it really depends on Macron and Trump,” said Mark Dubowitz, chief executive of the Foundation for Defense of Democracies. “It sounds narrow, but it’s actually pretty fundamental. It’s entirely possible that the thing breaks down on that basis.”

The Germans are the most resistant among the Europeans, arguing that renegotiating without Iran or the other parties to the deal, Russia and China, amounts to bad faith and ultimately will cause the original agreement to collapse. If no side agreements are reached, the Trump administration is also preparing contingency plans for Mr. Trump to withdraw from the Iran deal altogether and what the United States would then do to counter Iran.

Russia and China have resisted any changes. “We will obstruct attempts to sabotage these agreements, which were enshrined in a U.N. Security Council resolution,” Sergey V. Lavrov, the Russian foreign minister, said Monday after meeting with his Chinese counterpart, Wang Yi, in Beijing.

But critics of the deal pressed Mr. Trump to remain strong. Prime Minister Benjamin Netanyahu of Israel on Monday again condemned the agreement. The deal “gives Iran a clear path to a nuclear arsenal” and “does not deal with the ballistic missiles that can deliver this weapon to many, many countries,” he said. “This is why this deal has to be either fully fixed or fully nixed.”