Tensions have risen between the world's two largest nuclear nations after the latest attempt to resolve the Ukraine war failed, with Russia carrying out tests of its nuclear-powered, nuclear-capable weapons systems and Trump saying he was ordering the test of atomic weapons.

He accused Moscow of having secretly carried out nuclear detonations -- not just the testing of delivery systems, which all nuclear-armed states do regularly.

"We are ready to discuss the suspicions raised by our American colleagues regarding the possibility that we might be secretly doing something deep underground," Lavrov told state media in a televised interview.

He denied Trump's claims and said the United States could check whether Russia tested a nuclear warhead via the global seismic monitoring system.

"Other tests, both subcritical, or those without a chain nuclear reaction, and carrier tests, have never been prohibited," Lavrov added.

Trump accused both Russia and China of testing nuclear weapons in an interview with US broadcaster CBS News earlier this month, after abruptly shelving a proposed summit with Putin on Ukraine.

But Lavrov said the two issues were not connected.

"I would not mix the topic of nuclear tests with the topic of the Budapest summit," he said.

He also said Moscow was still open to a possible meeting between Putin and Trump.

"We are ready to discuss with our American colleagues the resumption of preparatory work for the proposed summit of the leaders of Russia and the United States."

Trump has grown increasingly frustrated with Putin in recent months over the Kremlin chief's refusal to halt his almost four-year offensive against Ukraine.