Although Pompeo and Lavrov discussed a wide range of bilateral and international problems, including the situations in Iran, North Korea, Ukraine, Syria and Venezuela, they didn't have major breakthroughs on any of those issues.
At the joint news conference with Lavrov following the talks, Pompeo said Washington is willing to rebuild its relationship with Moscow, but it expects its Russian counterparts to act on it with all seriousness.
"President Trump's made it clear that his expectation is that we have an improved relationship between our countries. This will benefit each of our people. And I think that our talks here today were a good step in this direction", said Pompeo.
It is Pompeo's first visit to Russia as Secretary of State. After his meeting with Lavrov, the American diplomat met with Russian President Vladimir Putin.
The Russian leader said he had spoken to U.S. President Donald Trump several days ago, and he got the impression that Trump indeed "intends to rebuild U.S.-Russian relations and contacts in order to solve the issues of mutual interest."
"On our behalf, we have said it multiple times that we also would like to rebuild fully fledged relations, and I hope that right now the conducive environment is being built for that," Putin said to Pompeo.
Putin then brought up the special counsel Robert Mueller's investigation into Russian election interference by calling it "exotic work." Putin denied any collusion between his government and the current U.S. administration.
Earlier, during the joint press conference after talks with Lavrov, Pompeo issued a few stern warnings to Moscow, saying it should refrain from interfering in the 2020 U.S election, free captured Ukrainian sailors and try to make peace with Kyiv.
He also said the two sides disagree on Venezuela and urged Russia to end its support for President Nicolas Maduro. Washington and 50 other countries have recognized opposition leader Juan Guaido as Venezuela's interim leader.
Tuesday's Sochi meeting came after Pompeo shared intelligence and details with European allies about what the United States calls Iran's recent "escalating threat," blaming Tehran for failing to choose talks over threats.
"And we want to make sure (Europeans) understood the risks as we saw them, and I shared that with them in some detail. As for our policy, it's been consistent now for the entire Trump administration and the decision to withdraw from the JCPOA [Iran nuclear deal], now just over a year ago, made clear what our objectives are", said Pompeo about his stopover in Brussels en route to Sochi.
The top U.S. diplomat called on the Iranian regime to "behave like a normal country" and accused its leadership of conducting "assassination campaigns throughout Europe" and "supporting the Hezbollah."
Before the meeting, State Department Special Representative for Iran Brian Hook told reporters Iran "plays a destabilizing role in Syria" and that Iran's use of Syria "as a missile platform to advance its foreign policy objectives" goes against Russian goals of bringing stability to the Syria.
Russian forces have been aiding the Syrian military since 2015, while Iran has been a major backer of President Bashar al-Assad, giving support and training to Shi'ite militias.
Analysts say they did not expect any surprise breakthroughs on Iran in Sochi.
"Tehran is an important strategic ally of Moscow in Syria," said Gleb Pavlovsky, the president of the Moscow-based Russia Institute. "I do not anticipate any changes there, because Russia without Iran in the Middle East would be ‘naked.’ Something should have been offered to Moscow. I am hoping (Pompeo) came to offer some kind of exchanges, tradeoffs political or economic."
The head of the Russian International Affairs Council, Andrey Kortunov, said Washington should not seek support on its Iran foreign policy in Moscow for a number of reasons.
"How can they reach any compromise here? Russia cannot support the U.S. sanctions toward Iran for a number of reasons, primarily because it is under such pressure itself. Trump, of course, would have liked if Russia used its leverage over Iran's behavior in the region," says Kortunov.
Experts believe the meetings in Sochi demonstrated that even in cases when U.S. and Russian interests overlap in certain parts of the world, it should be viewed as a mere coincidence, rather than a pattern.
"We are talking about some situational convergence, and not about a unified vision of the global picture," concludes Kurtunov.
Pompeo's trip comes a few weeks ahead of a Group of 20 summit meeting June 28-29 in Osaka, Japan, with both Putin and President Trump expected to attend. Trump said on Monday he will meet with Putin on the sidelines of the G-20 summit.