"If the Russians were engaged in that in 2020, it would put our relationship in an even worse place than it has been", said Pompeo.
Pompeo agreed that there are matters of mutual interest between the United States and Russian Federation, where both countries can work together productively.
Pompeo, who visited Pyongyang four times previous year, has taken a leading role in seeking to negotiate an accord with North Korea under which the authoritarian state will give up its nuclear arsenal.
"And we should expect in 2050, the Russians will be at it still", he said.
As well as the issue of interference in USA elections, the two sides clashed over Venezuela, with Lavrov sharply criticizing Washington for trying to undermine President Nicolas Maduro, who Pompeo said must step down in the face of an economic crisis and large-scale protests against his rule.
Pompeo - who like most of the U.S. political class, with the major exception of President Donald Trump, has been outspoken in his criticism of Putin - said that the two countries found areas on which to cooperate, and voiced optimism in breaking a deadlock on Syria.More news: Deepest-ever manned dive ‘finds plastic bag at bottom of Mariana Trench’
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Putin hailed the two-year investigation by special counsel Robert Mueller that did not find collusion by the Trump campaign - but documented extensive meddling by Russian Federation, especially by manipulating social media.
German Foreign Minister Heiko Maas said he had told Pompeo during their Monday meeting: "We do not want it to come to a military conflict (between the United States and Iran)". Meanwhile, Secretary of State Mike Pompeo conveyed President Donald Trump's interest in restoring better ties. He also was critical of USA sanctions punishing countries doing business with Iran.
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. He also said the two sides disagree on Venezuela and urged Russian Federation to end its support for President Nicolas Maduro.
Washington previous year pulled out of a nuclear deal backed by Europe, Russia and China, which curbed Iran's nuclear ambitions in return for sanctions relief.
Iran recently threatened to resume higher enrichment in 60 days if no new nuclear deal is in place, beyond the 3.67% permitted by the current deal between Tehran and world powers.
Hunt, who held talks with Maas and Le Drian on the margins of a regular European Union meeting in Brussels, expressed concern about the risks of a nuclear arms race in the Middle East if Iran were to acquire such weapons. Trump said on Monday that he will meet with Putin on the sidelines of G-20 summit.