Peace talks on ending the nearly three year war in Ukraine are due to start in the coming days after US President Donald Trump shocked European allies by calling Russian President Vladimir Putin this week and declaring an immediate start to the talks.
During the call on Saturday, which was initiated by the US side, Lavrov and Rubio agreed to work on restoring "mutually respectful interstate dialogue" in line with the tone set by the presidents, the Russian foreign ministry said in a statement.
The two agreed to maintain contacts to resolve problems in bilateral relations, "in the interests of removing the unilateral barriers to mutually beneficial trade, economic and investment co-operation inherited from the previous administration", the statement said.
It was not immediately clear what specific barriers were discussed.
"The two sides expressed their mutual willingness to interact on pressing international issues, including the settlement around Ukraine, the situation around Palestine and in general in the Middle East in general."
Rubio, national security adviser Mike Waltz and White House Middle East envoy Steve Witkoff will travel to Saudi Arabia, US Representative Michael McCaul told Reuters.
Ukrainian President Volodymyr Zelenskiy, who met with US Vice President JD Vance in Germany on Friday, said he was not invited to the talks in Saudi Arabia and Kyiv would not engage with Russia before consulting with strategic partners.
Meanwhile, European leaders are planning to hold a special summit in Paris about the conflict in Ukraine in response to Trump's plans to end to the war.
"There are ongoing talks between leading European politicians about a possible informal meeting, but nothing has been finalised yet," the Élysée Palace said.
The US under former President Joe Biden and Kyiv's allies across the world imposed waves of sanctions on Moscow over its invasion of Ukraine three years ago, aimed at weakening the Russian economy and limiting the Kremlin's war efforts.
Trump and Putin spoke for over an hour on Wednesday, the first known direct contact between US and Russian presidents since Putin had a call with Biden shortly before ordering tens of thousands of troops into Ukraine in February 2022.
The Russian foreign ministry also said that Lavrov and Rubio discussed also how to tighten the conditions for the functioning of Russian diplomatic missions" in the US.
"It was agreed to organise a meeting of experts in the very near future to agree on specific steps to mutually remove obstacles to the work of Russian and US missions abroad," the ministry said in its statement.