Pompeo warned Russian Federation not to meddle in the U.S. presidential election next year, calling on Moscow "to demonstrate that these types of activities are a thing of the past".
Pompeo earlier told Russian Foreign Minister Sergei Lavrov that U.S. President Donald Trump was committed to improving relations with Moscow.
Trump stunned Russian officials in November by scrapping a meeting with Putin at last year's G20 summit in Argentina with a Twitter announcement the day before the talks, blaming tensions over Russia's capture of Ukrainian sailors.
"We are talking about some situational convergence, and not about a unified vision of the global picture", said the head of the Russian International Affairs Council, Andrey Kurtunov. "I hope that, today, the situation is changing".
"We of course heard President Trump's statement that he expects to hold a meeting with President Putin, " Lavrov said in the news conference. "If Russia were to engage in that in 2020, it would put our relationship in an even worse place than it is". We have encouraged them not to.More news: Madonna rejects calls for Tel Aviv Eurovision boycott
"We would not tolerate that. Our elections are important and sacred and they must be free and fair".
"There are also no agreements so far", Kremlin spokesman Dmitry Peskov told the Interfax news agency. "It's about trying to find solutions, compromises, places where there are overlapping interests you can make progress unlocking some of the most hard problems that are facing us".
Putin told Pompeo his recent telephone conversation with Trump raised hopes for an improvement in relations. "But the implementation of the agreement, which was reached a few months ago, is in full swing", he said.
"Some of our cooperation has been excellent - on North Korea, on Afghanistan, we've done good work - (and) counter-terrorism work - together. We have differences and each country will protect its own interests, look out for its own interests of its people".
Pompeo meanwhile said he had urged Lavrov to end Russia's support for Venezuelan President Nicolas Maduro. These are the things we can build upon. "We want every country that's interfering in Venezuela to cease doing that".
Iran was one of the key items on the agenda because of tensions in the region rising.More news: Serena Williams pulls out of Italian Open with knee injury
Ties between the two countries have been damaged by allegations - denied by Moscow - that Russian Federation tried to influence the results of the 2016 United States presidential election, and by differences over Iran, Syria, Ukraine and Venezuela.
To deter those threats and counter any possible attack, the US sent an aircraft carrier and B-52 bombers to the Middle East, heightening already high levels of unease caused by the re-imposition of USA sanctions on Tehran following Trump's withdrawal of the US from the 2015 Iran nuclear deal a year ago.
His inquiry had cast a pall over U.S.
US Secretary of State Michael Pompeo on Tuesday said his country is not seeking war with Iran, despite a spike in tensions that has seen the Pentagon dispatch nuclear-capable bombers to the region.
But Pompeo added: "We have also made clear to the Iranians that if American interests are attacked, we will most certainly respond in an appropriate fashion".
"As soon as Iran takes its first reciprocal steps and says that it is leaving, everyone will forget by tomorrow that the USA was the initiator of this collapse, Iran will be held responsible, and the global public opinion will be intentionally changed in this direction", Putin said.More news: AEW Coming To TNT