During a press conference with Secretary of State Mike Pompeo, Putin shared his thoughts on the Mueller probe.
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".
"We need to make sure that we don't end up putting Iran back on the path to re-nuclearisation", Hunt said, calling for "a period of calm so that everyone understands what the other side is thinking".
Pompeo also said he urged Russian Federation to end its support of Venezuelan dictator Nicolas Maduro.
President Trump, though, was less assuring. He also was critical of USA sanctions punishing countries doing business with Iran.
In the highest-level face-to-face contact between the two countries since special counsel Robert Mueller's report was released last month, Putin told Pompeo he hoped relations with the US would now improve. "If American interests are attacked, we will most certainly respond in an appropriation fashion", said Pompeo.
"We've said many times that we also want to fully restore our relations".
Pompeo, speaking earlier at a joint news conference with Foreign Minister Sergei Lavrov, acknowledged deep differences on election meddling - and warned Russian Federation to stay out of next year's vote.
The report by USA special counsel Robert Mueller did not find Trump's campaign team colluded with Moscow but did document widespread Russian attempts to influence the 2016 election.
They also discussed North Korea, which both want to see give up its nuclear weapons.
Pompeo said Trump had made clear he wanted the to try to keep the Russian Federation relationship "on the high ground".
Last week, Washington announced the deployment of an aircraft carrier battle group and a bomber task force to the Persian Gulf to counter what US officials called "clear indications" of Iranian threats to the interests of the United States or its allies in the region.
"On Venezuela, we have disagreement", Pompeo said. "It's about trying to find solutions, compromises, places where there are overlapping interests".
Russian Foreign Minister Serguei Lavrov has rejected US threats against the Venezuelan government and said it has nothing to do with democracy.
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.
"We fundamentally do not seek a war with Iran", he said.
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. Russian Federation has interests in oil projects in Venezuela and has propped up Mr Maduro's regime with loans.