Putin did not address Mueller's conclusion that Russian Federation actively interfered in the election.
During Pompeo's visit, Russian Foreign Minister Sergei Lavrov said Moscow would work "to ensure this situation does not descend into a military scenario".
Pompeo was the highest-ranking American to see Putin since July when the Russian leader met in Helsinki with Trump - who shocked the United States establishment by seeming to take at face value Putin's denials of election interference. Iran has denied that they are interested in war.
Pompeo, on his first visit to Russian Federation as the top USA diplomat, said the Trump administration is committed to improving ties and wants to work together where the two countries have what he called "overlapping interests".
Pompeo underlined to Putin that Trump wanted to make "our two peoples more successful and, frankly, the world more successful, too". Russian Federation is one of the remaining signatories, and Lavrov is likely to stress to Pompeo the deal's importance for global security.
Iran was one of the key items on the agenda because of tensions in the region rising. "It's not destined that we're adversaries on every issue". The U.S. has accused Iran of threatening to attack American interests in the Middle East and suggested that Iran or Iranian proxies are behind incidents of alleged sabotage on Emirati, Norwegian and Saudi tankers in the Persian Gulf.
Moscow and Washington are overdue to dispel "suspicions and prejudices on both sides", Lavrov said, and to "start building a new constructive framework" of how Russian Federation and the U.S see each other.
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".
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.
Pompeo - who just three days earlier in a speech said that "the Putin regime slays dissidents in cold blood" - said he was not trying to reconcile but rather to find common interests.
One such situation is the conflict in Syria, where Russian Federation has supported President Bashar al-Assad's forces, while the United States has backed rebels who want to see Assad out of office. U.S.
"We fundamentally do not seek war with Iran, " Pompeo said.
Lavrov said the Mueller report and "baseless" allegations of Putin-Trump collusion in the 2016 election had "frozen" the relationship. "We said we are open to any contacts and will wait for the specification of the proposal", Ushakov said.