The United States and Russia edged toward an arms control deal Tuesday after Moscow agreed to a freeze on the number of nuclear warheads on each side and to extend the accord known as New START for one year.

The breakthrough came days after the two sides appeared to have nearly given up on finding a compromise and as President Trump urges his aides to bring him foreign policy wins in the final stretch of the U.S. presidential campaign.

Russia's Foreign Ministry put forward the proposal Tuesday, and within hours, the State Department expressed gratitude for the offer and requested an immediate meeting of negotiators.

"We appreciate the Russian Federation's willingness to make progress on the issue of nuclear arms control," State Department spokeswoman Morgan Ortagus said in a statement. "The United States is prepared to meet immediately to finalize a verifiable agreement. We expect Russia to empower its diplomats to do the same."

Negotiators would still need to work out a verification system and agree on the definition of a warhead, which are "not small details," said Daryl Kimball, the executive director of the Arms Control Association.

“It’s not a dramatic breakthrough by any means,” he added, “but it would avoid the total collapse of the U.S.-Russian arms control system and would give Washington and Moscow time to continue to engage in further complex and lengthy talks.”

A warhead freeze was a condition demanded by the Trump administration, which on Friday rejected Russian President Vladimir Putin’s offer of a one-year extension of New START, a 10-year accord that places limits on the two countries’ nuclear warheads.

Putin’s proposal Friday made no mention of a mutual freeze on nuclear stockpiles, suggesting instead a simple one-year extension of the treaty with no conditions while Moscow and Washington negotiate what comes next.

U.S. national security adviser Robert C. O’Brien responded in a statement that the offer was a “non-starter,” adding, “We hope that Russia will reevaluate its position before a costly arms race ensues.”

Moscow seemingly acquiesced Tuesday. The Russian Foreign Ministry said in a statement that the country “proposes extending New START for one year, and at the same time, it stands ready, together with the U.S., to assume a political obligation on freezing a number of the nuclear warheads possessed by the parties for this period.”

“This item can be put into effect strictly and exclusively with the understanding that the freezing of warheads would not involve any extra requirements on the part of the U.S.,” the statement continued. It added that if Washington agrees, then “the time bought by extending New START can be used for conducting comprehensive bilateral negotiations on future control over nuclear missile weapons.”

The 2010 treaty, which expires in February, restricts the number of deployed strategic nuclear warheads and certain launch platforms. If the treaty is not extended or replaced, the world’s two biggest nuclear powers will return to an era without substantive restraints on their arsenals for the first time in decades. (START is an acronym for Strategic Arms Reduction Treaty.)

The treaty includes a clause that allows the leaders of both nations to extend the agreement by five years without requiring ratification. Democratic presidential nominee Joe Biden has said he would agree to the five-year extension if elected. Putin has also said he would agree to the extension, and in an interview with state television this month he said Biden’s willingness to prolong New START “is a serious signal for our possible future interaction.”

The Trump administration’s envoy for arms control, Marshall Billingslea, initially insisted that China participate in talks. He wanted any replacement treaty to include China and to encompass all of Russia’s nuclear weapons — not just the “strategic” weapons covered under New START but also Russia’s sizable stockpile of smaller, “tactical” nuclear weapons that fall outside the treaty. Billingslea also insisted that ­verification mechanisms for any ­follow-on treaty be strengthened.

Russia rejected the demands, and China has refused to take part in negotiations.

Trump then dispatched O’Brien to meet with his Russian counterpart, Nikolai Patrushev, early this month in Geneva.

After that meeting and calls between Trump and Putin, the Trump administration thought an agreement in principle had been reached. Speaking last week at the Heritage Foundation, Billingslea said he hoped that the ­“gentleman’s agreement” would “percolate down through their system so that my counterpart hopefully will be authorized to negotiate.”

“We’re ready to strike this deal. We could strike it tomorrow, in fact,” Billingslea said. “But Moscow is going to have to show the political will to do so as well.”

Democrats welcomed the progress in the talks but urged the Trump administration to establish a mutual verification system and finalize an extension of New START.

“It is in the national interest of the United States to extend the New START treaty as we continue dialogue with both Russia and China on key nuclear issues,” said Sen. Robert Menendez (N.J.), the top Democrat on the Senate Foreign Relations Committee. “The real impact of a freeze on the total number of nuclear warheads will be unclear unless the Trump administration can ensure Russia sticks to the agreement’s terms through robust verification mechanisms.”

Khurshudyan reported from Moscow. Paul Sonne in Washington contributed to this report.