"We had a frank discussion about many issues including many places where we disagree", Pompeo said.
The US has sent further military forces to the Middle East, including an aircraft carrier, B-52 bombers and Patriot missiles, in a show of force against what US officials say are Iranian threats to its troops and interests in the region.
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". "These missiles could easily kill a Russian or an American", Pompeo said.
Lavrov said Russian Federation is hoping for a positive response from the United States about extending the New START arms control treaty, which is due to expire in 2021, "but we really have some concerns which are related to the re-equipping of launchers of Trident submarines and heavy bombers announced by the United States".
File photos of Iran's supreme leader Ayatollah Ali Khamenei (L) and US Secretary of State Mike Pompeo (R).
Mogherini chaired a meeting of the so-called E3 - Britain, France and Germany - to discuss efforts to keep the deal going, including the special trade mechanism called INSTEX the trio set up to try to enable legitimate trade with Iran to continue without falling foul of U.S. sanctions.
"It's clear that such insinuations are absolute fiction", he said after the talks with his U.S. counterpart.
Pompeo's trip has been seen as a precursor to a meeting between US President Donald Trump and Putin at the G20 summit in Osaka, Japan, next month.
But the pair had little to agree on in their statements to the press some three hours later.
"I hope that we can find places where we have overlapping interests and can truly begin to build out strong relationships", Pompeo said, citing the fight against terrorism and regional conflicts as potential areas for co-operation.
Lavrov however repeated Moscow's denials of interference and said it was "absolute fiction" that Russian Federation had colluded with the Trump campaign.
Pompeo meanwhile said he had urged Lavrov to end Russia's support for Venezuelan President Nicolas Maduro.
Russian Federation and the USA also do not see eye to eye when it comes to Syria, where government forces have been leading a major offensive against the last rebel-held province in recent weeks.
The exchange follows the publication of the Mueller report, which found that Russian Federation interfered in the 2016 United States election but did not conclude that the Trump campaign colluded with Moscow.
But Lavrov flatly rejected the request, denouncing U.S. and opposition "threats" against the Maduro government.
The US administration has kept up a campaign of pressure including sanctions on Russian Federation over the alleged election meddling and Moscow's support for armed separatists in Ukraine.