But Pompeo also named regions where he saw potential for the United States and Russian Federation to work together more closely.
U.S. Secretary of State, Mike Pompeo, was in Russia this week for a meeting with his counterpart, Russian Foreign Minister, Sergey Lavrov.
"If Russia engaged in that in 2020, it would put our relationship in an even worse place than it has been".
Pompeo was the highest-ranking American to see Putin since July when the Russian leader met in Helsinki with Trump - who shocked the U.S. establishment by seeming to take at face value Putin's denials of election interference.
"I had the impression that the president intends to rebuild US-Russian relations and contacts in order to solve issues of mutual interest, " Putin told Pompeo, referring to the call with Trump.
Pompeo underlined to Putin that Trump wanted to make "our two peoples more successful and, frankly, the world more successful, too".
"We see that there are suspicions and prejudices", Lavrov told Pompeo at the start of their talks.
"Some of our cooperation has been excellent, on North Korea, on Afghanistan, " Pompeo told Putin.
Pompeo meanwhile said he had urged Lavrov to end Russia's support for Venezuelan President Nicolas Maduro. Russian Federation is one of the remaining signatories, and Lavrov is likely to stress to Pompeo the deal's importance for worldwide security. "These are things we can build upon".
Iran was one of the key items on the agenda because of tensions in the region rising.
"We have many differences here but the fact we will continue to discuss the situation that gives us hope that certain agreements could be reached with the support of the United States and Russia", Lavrov said, according to CBS News.
Experts said the meetings in Sochi demonstrated that even in cases when US and Russian interests overlap in certain parts of the world, it should be viewed as a mere coincidence, rather than a pattern.
His remarks come after the United States deployed an aircraft carrier strike group and nuclear-capable B-52 bombers to the Middle East, although President Donald Trump denied a report that he is considering sending 120,000 troops.
His inquiry had cast a pall over U.S.
"We fundamentally don't seek war with Iran", Pompeo said.
But he added: "We have also made clear to the Iranians that if American interests are attacked, we will most certainly respond in an appropriate fashion".
Hanging over Trump's quest for warm ties with Russian Federation have been persistent allegations that his campaign worked with the rival power to swing the 2016 election to the mogul over his rival Hillary Clinton. But Putin's aide Yuri Ushakov said they did not touch on Ukraine, where Russia's backing of separatist rebels have prompted USA sanctions.