The US will not tolerate Russian meddling in the 2020 presidential elections, Secretary of State Mike Pompeo told the Russian Foreign Minister in talks on Tuesday, after both said they wanted warmer relations.
Earlier, Russian Foreign Minister Sergey Lavrov called on the US to set aside its differences with the Kremlin to mend ties.
Mr Pompeo is in Russia on this first official visit since taking up the post.
"We see that there are suspicions and prejudices," Mr Lavrov told Mr Pompeo on Tuesday afternoon in Sochi
"This hinders both your security and our security and causes concern around the world. We think it is time to build a new and more constructive matrix for our relations.
"We are ready to do that if our US colleagues are ready to reciprocate.”
Mr Lavrov said the tension between the two countries had a negative effect on global affairs and it was important to Russia "to rebuild the channel of communications" with the US.
Mr Pompeo arrived in Sochi on Tuesday, a day later than planned after a last-minute detour to Brussels to lobby against Iran on Monday, forgoing talks with US embassy staff and members of the American business community in Moscow.
Mr Pompeo told Mr Lavrov that US President Donald Trump was committed to improving ties with Russia.
“We have differences and each country will protect its own interests, look out for its own interests of its people,” he said.
"But it's not destined that we're adversaries on all issues and I hope that we can find places where we have a set of overlapping interests and continue to build out strong relationships, at least on those particular issues."
Moscow’s relationship with Washington deteriorated after Russia’s annexation of the Crimean Peninsula from Ukraine in 2014.
Western governments responded with harsh economic sanctions on Russia.
They have intensified those sanctions after evidence surfaced that Russia meddled in the 2016 US presidential elections and the poisoning of former Russian spy Sergei Skripal in the UK last year.
Before the talks on Tuesday, Mr Pompeo seemed to strike a conciliatory tone in a tweet that said the meetings in Sochi would cover a range of topics.
“On some issues we may agree, on others we may disagree,” he wrote. “But when it’s in our national interests, it is our responsibility to find a way forward.”
That tone was not matched by officials in Moscow. The Kremlin dismissed an earlier White House announcement that Mr Trump and Mr Putin would meet on the sidelines of the G20 Summit next month in Japan.
Kremlin spokesman Dmitry Peskov said there had been no discussion of such meeting, let alone an agreement.
Mr Trump abruptly cancelled his last meeting with Mr Putin before last year’s G20 summit in Argentina, blaming a flare-up of tension in Ukraine.
Mr Lavrov and Mr Pompeo also spoke about Syria, Iran and Venezuela, on which they continued to disagree.
"I urged my Russian colleagues to support the Venezuelan people as they return democracy to their country," Mr Pompeo said.
"The US and more than 50 other nations agree that the time has come for [President] Nicolas Maduro to go.
"He has brought nothing but misery to the Venezuelan people and we hope that the Russians’ support for Maduro will end."
But despite the disagreements, Mr Pompeo said the US would "keep talking" to Russia about Venezuela's political transition.
Russian deputy foreign minister Sergei Ryabkov said on Monday that Moscow wanted to discuss extending the Start Treaty, which limits nuclear arsenals and is due to expire in 2021.
This year, Russia and the US scrapped their obligations under the Intermediate-Range Nuclear Forces Treaty, the only surviving Soviet-era arms control agreement.
On Tuesday morning, the head of the Russian Foreign Ministry’s department of arms control and non-proliferation seemed to throw fuel on the fire, claiming that the US was preparing to set up and use nuclear weapons in Europe.
“Sadly, some countries dependent on Washington pretend that nothing is happening or are simply afraid to think about how provocative this act is,” Vladimir Yermakov told state news agency RIA Novosti.
The Kremlin on Tuesday dismissed as a “conspiracy theory” the idea that Mr Putin’s tour of a weapons base near Sochi was meant to send a signal to the visiting US officials.