The accord, known as the Joint Comprehensive Plan of Action, severely limited Iran’s nuclear activities in return for ending or easing many sanctions that were hurting the Iranian economy.
Under an American law, Mr. Trump must recertify every 90 days that Iran is complying with the nuclear accord, or the American sanctions that were lifted could be reinstated. The next 90-day deadline is in mid-October.
When he reluctantly signed the last recertification in July, Mr. Trump said “if it was up to me, I would have had them noncompliant 180 days ago.”
The possibility that Mr. Trump may find a reason to declare Iran noncompliant, regardless of the merits, alarmed the nonproliferation experts.
They warned in their statement that “unilateral action by the United States, especially on the basis of unsupported contentions of Iranian cheating, would isolate the United States.”
Last week, Mr. Trump’s ambassador to the United Nations, Nikki R. Haley, suggested in a Washington speech that the president would be justified in decertifying Iran even if it was technically honoring the accord.
Iranian officials have said that any resumption of the nuclear-related sanctions by the United States would violate the accord.
Whether that would lead to its unraveling is unclear, but President Hassan Rouhani of Iran has suggested the country could quickly restore the nuclear-fuel enrichment capabilities that had been limited by the agreement.
The signers of the statement urging Mr. Trump to respect the agreement are experts in nuclear nonproliferation diplomacy from around the world.
They included Nobuyasu Abe, commissioner of the Japan Atomic Energy Commission; Hans Blix, former director general of the International Atomic Energy Agency, Thomas E. Shea, a former safeguards official at the International Atomic Energy Agency; and Thomas M. Countryman, a former assistant secretary of state for international security and nonproliferation.
The statement was organized by the Arms Control Association, a disarmament advocacy group based in Washington.
The Trump administration’s concerns with Iran have come as the United Nations Security Council, prodded by the United States, has ratcheted up pressure on North Korea to stop its nuclear and missile testing and resume disarmament talks.
Kelsey Davenport, the director for nonproliferation policy at the Arms Control Association, expressed worry that if the administration abandoned the Iran agreement, any possibility of inducing North Korea to negotiate would be lost.
“Given that we are already struggling to contain the North Korean nuclear and missile crisis, it would be extremely unwise for the president to initiate steps that could unravel the highly successful 2015 Iran nuclear deal, which would create a second major nonproliferation crisis,” he said.