On Thursday, top US diplomat Antony Blinken warned Russia against entering Ukraine, as Moscow told Kiev that any attempt to retake the Crimean peninsula amounted to a direct threat to Russia.
In recent weeks, Western powers have been alarming about Russian troops along the border with Ukraine, further stoking tensions in an area where a long-running conflict has already left 13,000 dead.
Moscow, accused of backing the separatists fighting Kiev, denies preparing an attack and accuses NATO of raising the temperature.
Blinken told Lavrov in talks on Thursday near Stockholm that the US was ready to facilitate the full implementation of the Minsk peace accords, because they have deep concerns about Russia's plans for renewed aggression against Ukraine.
The Minsk deal was reached after Russia annexed Crimea in 2014 and aimed at resolving the conflict with pro-Russian separatists in eastern Ukraine, but was never enforced.
Diplomacy is the best way to avert a crisis, according to Blinken.
The US, Russia and Ukraine were all in Stockholm on Thursday for a meeting of the Organisation for Security and Cooperation in Europe, OSCE, one of the few international dialogue forums that both the US and Russia belong to.
In the plenary session, Blinken called for Moscow to de-escalate, reverse troop build-up and return forces to normal peaceful positions. Lavrov said that the nightmare scenario of a military confrontation was returning in Europe, accusing NATO of inching its military infrastructure closer to Russia's borders.
He reiterated his opposition to any NATO expansion eastward, including Ukraine, but said Russia was open to dialogue.
He said that they were interested in the joint efforts to find a resolution to the Ukraine crisis.
The OSCE meeting took place amid spiking tensions, despite the cordial tone.
At a NATO meeting in Latvia on Wednesday, Blinken accused Russia of trying to destabilise Ukraine from within as well as large military operations. He said Russian President Vladimir Putin had decided to invade but he said he did not know if he would put in place the capacity to do so on short order. Blinken warned that there would be far-reaching consequences for Moscow if it pushed ahead with any aggression, including a number of high-impact economic measures which we have refrained from using in the past. On Thursday, he spoke with Ukrainian Foreign Minister Dmytro Kuleba, who said his country would demonstrate restraint, but he also called on Kiev's partners to prepare a deterrence package that would make Russia think twice before resorting to military force.
Ukrainian President Volodymyr Zelensky said on Wednesday that Crimea was Ukrainian territory and Kiev's goal was to liberate it.
The Kremlin spokesman Dmitry Peskov told reporters on Thursday that they see this as a direct threat to Russia.
On Thursday, tensions continued on the ground outside the diplomatic forum.
A Ukrainian soldier was killed in clashes with pro-Russian separatists, Kiev said, while Moscow announced it had arrested three Ukrainian spies, including one it said had planned a terrorist attack.
The OSCE meeting was planned long in advance but comes at a crucial moment as tensions in Europe mount on a number of issues.
In addition to Ukraine, there are other issues on the agenda that include the migrant crisis on the Belarus-EU border and the resurgence of clashes between OSCE members Armenia and Azerbaijan.
The US State Department said the EU reached an agreement on new sanctions against Belarus on Wednesday, and that the US would follow suit soon.
Unanimity is required in the plenary session of the OSCE, as it is not expected to lead to the adoption of any major agreements.
A planned resolution on Ukraine was scrapped because of a lack of consensus.