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.