On Syria, Lavrov said representatives from the new U.S. administration had been invited to take part in peace talks slated for Jan. 23 in Kazakhstan.
He hoped U.S. officials would attend, he said, as that would be the first opportunity for Moscow and Washington to start talking about closer Syria cooperation.
Moscow backs President Bashar al-Assad in the Syria conflict while Washington supports rebels opposing him, but both have a common enemy in Islamic State militants.
Lavrov questioned however whether Trump, in an interview he gave to The Times of London, had really suggested he would be ready to drop U.S. sanctions on Moscow in exchange for nuclear arms cuts saying his own reading of the interview had not suggested any linkage between the two issues. [nL5N1F50VI]
But he said Moscow wanted to start talks with the United States on nuclear weapons and on the balance of military power between the two former Cold War foes anyway.
"It's one of key themes between Russia and the United States. I am convinced we will be able to restart a dialogue on strategic stability with Washington that was destroyed along with everything else by the Obama administration."
Such talks could cover hypersonic weapons, the U.S. anti-missile shield in Europe, space weapons, and what he said was the U.S. refusal to ratify a ban on nuclear testing. Trump has called for a nuclear weapons build-up.
Some commentators have said Senate hearings for some of Trump's picks show they will be tough on Russia. But Lavrov said he had been encouraged by Rex Tillerson, the incoming Secretary of State, whom he cited as saying Moscow's
behaviour was not unpredictable.
"(That) means that we are dealing with people who won't get involved in moralising, but will try to understand their partner's interests," Lavrov said.
Tillerson had extensive dealings with Russia when he was the head of Exxon Mobil oil company.