But that was one of the few things the leaders appeared agree upon - their subsequent press conference revealed a number of areas where the two countries could not come to a consensus.
Russian Federation is one of the remaining signatories, and Lavrov is likely to stress to Pompeo the deal's importance for worldwide security. "I hope that Russian Federation takes advantage of those opportunities", he said.
While the European Union shares some USA concerns about Iran, including over its involvement in the Syrian conflict, it still backs the 2015 nuclear deal, saying that it is in Europe's own security interests.
Amid growing concerns of a conflict between the United States and Iran, U.S. officials have told their European allies that its military buildup in the Persian Gulf region is a "defensive" move in response to multiple threats coming out of Iran.
Iranian President Hassan Rouhani warned last week Tehran could resume enrichment of nuclear fuel at a higher grade if the European powers, China and Russian Federation did not do more to circumvent punitive USA measures on banking and energy to boost trade. "We want the regime to stop conducting assassination campaigns".
Pompeo added that reports of USA movement of over 100,000 troops to the region would be left up to the Department of Defense. "That continues to be the case", said Pompeo's top Iran adviser, Brian Hook. Lavrov, however, hoped that those reports were "just rumors".
Speaking for almost two hours late into the evening in Putin's forested dacha in the Black Sea resort of Sochi, Pompeo became the highest-ranking American to meet the Russian leader in 10 months.
"We want every country interfering in Venezuela to cease doing that".
At least one, British Foreign Secretary Jeremy Hunt, said he feared that unintentional escalation from the USA and Iran could spark a conflict - an unusually bold statement that appeared to assign equal culpability to Washington and Tehran. He also said the two sides disagree on Venezuela and urged Russian Federation to end its support for President Nicolas Maduro.
"Democracy cannot be done by force". "The threats which we hear to Maduro's government now from official representatives of the USA administration and from Mr Guaidó, who is constantly reminding of his right to invite military intervention from outside - these have nothing in common..."
Meeting with Russian Foreign Minister Sergei Lavrov earlier in the day, Pompeo said that Washington would tolerate no interference by Moscow in the 2020 USA presidential election.
President Trump, though, was less assuring. "We heard a proposal - if we receive such an official invitation we'll respond positively", said Lavrov.
The EU's chief diplomat, Federica Mogherini, coolly announced she had a busy day and that the pair would talk "if we manage to arrange a meeting".
Pompeo did not specifically mention election meddling in his brief reply to Putin, although he did say the Trump administration would "protect our nation's interest". "I hope that the necessary conditions for that to happen will now be created".
Lavrov also denied any Russian interference in the USA election. These included Iran, Syria and Venezuela, where the United States supports opposition leader Juan Guaido as interim president and Russian Federation backs President Nicolas Maduro.
"It's clear that such insinuations are absolute fiction", he said after the talks with his United States counterpart.
"I made clear to Foreign Minister Lavrov. that interference in American elections is unacceptable". He added that the USA would not tolerate similar engagement in the upcoming 2020 election.
"I've formed the impression that your president wants to fix Russia-U.S. ties and contacts and wants to solve issues which are of common interest for us", Putin told Pompeo.