Sergei Lavrov said the agenda for such negotiations should also include new hypersonic weapons, a US missile shield in Europe, space weapons and nuclear testing.
In an interview with The Sunday Times, Mr Trump said he will consider reviewing US sanctions on Russia if President Vladimir Putin is prepared to reduce its stockpile of nuclear weapons.
"For one thing, I think nuclear weapons should be way down and reduced very substantially, that’s part of it," he said.
"But Russia’s hurting very badly right now because of sanctions, but I think something can happen that a lot of people are gonna benefit."
The Russian minister also commented on Mr Trump's statement suggesting he might consider lifting sanctions against Russia if it is willing to make nuclear arms cuts.
Mr Lavrov said he saw Mr Trump's statement as an offer to engage in nuclear arms control talks and help lay the groundwork for them by reviewing the issue of US sanctions against Russia.
He argued some commentators misinterpreted Mr Trump's remarks, saying he didn't see them as an offer to cut arms in exchange for cancelling the sanctions.
Mr Lavrov said Russia was ready to meet with Donald Trump's administration to discuss these issues after the US President-elect takes office.
He also described as a charlatan the former British spy who wrote a dossier on Mr Trump's alleged links to Russia.
He said allegations of Russian cyber attacks are fabricated, and suggested US intelligence agencies who tried to prove the President-elect had links to Russia should be fired.
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