At a European security conference in Sweden, Lavrov floated the idea of a new European security pact to try to stop NATO from expanding further east, BBC wrote.
US Secretary of State Antony Blinken warned of “serious consequences” if Russia sought conflict with Ukraine.
The meeting comes as Russia boosts its military near Ukraine’s border. Ukraine says Russia has amassed more than 90,000 troops there. Moscow denies it is preparing an attack on Ukraine and accuses Kiev of its own military build-up.
Lavrov and Blinken met at a conference of the Organisation for Security and Cooperation in Europe (OSCE).
US officials said the two sides had agreed to further dialogue on Ukraine.
Blinken hinted at the possibility of direct talks between US President Joe Biden and his Russian counterpart Vladimir Putin in the near future.
Russia’s Foreign Ministry hoped a Putin-Biden summit would take place in the coming days but no date had been set, Interfax reported.
Earlier this week, President Putin said Russia would seek US guarantees that NATO will limit its presence in Ukraine, which is not a member of the security alliance.
But on Thursday, Lavrov said in a speech that NATO was refusing to constructively consider proposals to de-escalate tensions and prevent dangerous incidents.
“The alliance’s military infrastructure is being irresponsibly brought closer to Russia’s borders in Romania and Poland, deploying an anti-missile defence system that can be used as a strike complex,” he said.
“American medium-range missiles are about to appear in Europe, bringing back the nightmare scenario of a military confrontation.”
He warned NATO against turning countries neighboring Russia, i.e. Ukraine, into “bridgeheads of confrontation”, and said he hoped Russian proposals for a new security pact would be carefully considered.
At a joint news conference with the Russian foreign minister, Blinken said the best way to avoid a crisis was through diplomacy and urged Russia to pull back its forces.
“The United States is willing to facilitate that but... if Russia decides to pursue confrontation there will be serious consequences,” he added.