Negotiations between the world's two largest nuclear powers have been left at an impasse amid tensions over the Ukraine conflict.
Moscow pulled out of the last remaining arms control agreement with Washington, called "New START", in 2023 amid a sharp deterioration in relations between the two countries.
Both have indicated they will unilaterally adhere to the warhead limits outlined in the treaty until 2026, but they are yet to agree on a replacement and talks have stalled for months.
"We are interested in starting this negotiation process as soon as possible," Kremlin spokesman Dmitry Peskov said Friday.
"The ball is in the Americans' court, who have stopped all substantive contacts," he added.
In remarks at Davos on Thursday, Trump said he would also want China involved in talks on nuclear arms control.
"We'd like to see denuclearization," Trump said, adding that Russian President Vladimir Putin "really liked the idea of -- of cutting way back on nuclear" during Trump's first term in office.
"China would have come along too. China also liked it," Trump said, warning that Beijing's nuclear arsenal would catch up with Washington's "at some point over the next four or five years."
"So, we want to see if we can denuclearize, and I think that's very possible," Trump said.
Putin has ramped up his nuclear rhetoric since sending troops into Ukraine in February 2022, signing a decree last year lowering the threshold for using nuclear weapons.
New START restricted the former Cold War rivals to a maximum of 1,550 deployed warheads each.
In 2019 the two powers withdrew from the landmark 1987 Intermediate-Range Nuclear Forces (INF) treaty concluded by then-US President Ronald Reagan and Soviet leader Mikhail Gorbachev, which limited the use of medium-range missiles, both conventional and nuclear.
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