Sergey Lavrov has said Russia is inviting representatives of the incoming US administration to attend upcoming Syria talks in Kazakhstan's capital.
Speaking on Tuesday in Moscow, the Russian foreign minister praised what he called Donald Trump's focus on combating "terrorism".
"By concentrating on a pragmatic search for mutual interests we can solve a lot of problems," he said.
He voiced hope that Russian and US experts could start discussions on "fighting terrorism" in Syria in Astana when Syrian government and opposition representatives meet there for talks on Monday.
He said: "We hope that the new administration will be able to accept that proposal," adding that the talks in Astana will offer "the first opportunity to discuss a more efficient fight against terrorism in Syria".
Lavrov said Russia expects that cooperation on settling the Syrian crisis will be more productive than it was with the administration of President Barack Obama.
"What we hear from Donald Trump [on Syria] and his team speaks to how they have a different approach [to Obama] and won't resort to double standards," he said.
Al Jazeera's James Bays, reporting from Washington DC, said Russia seemed to be trying to "lock in what it sees are military gains that it and the Assad regime have made in the recent months.
"Astana talks is where Russia believes it has influence. Russia will be controlling the process.
"It hopes to turn the diplomatic situation in a peace deal in the same way as it managed to turn the military situation to Russia's advantage".
With regard to the interview Trump has given to The Times of London, Lavrov questioned whether the US president-elect had really suggested he would be ready to drop US sanctions on Russia in exchange for nuclear arms cuts.
He said his own reading of the interview did not suggest any linkage between the two issues.
But he said Russia wanted to start talks with the US 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 US anti-missile shield in Europe, space weapons, and what he said was the US 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.
However, Lavrov said he had been encouraged by Rex Tillerson, the incoming secretary of state, whom he cited as saying Russia'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.
Source: Al Jazeera and news agencies