SOCHI, Russia — Secretary of State Mike Pompeo said he came to this Black Sea resort city on Tuesday on a mission for President Trump: Improve U.S. ties with Russia.

But as the night wore on at Russian President Vladimir Putin’s residence, it appeared that Pompeo could hope for little more than to depart Sochi having agreed to disagree. 

“There are places that our two countries can find where we can be cooperative, we can be productive, we can be accumulative, we can work together to make each of our two peoples more successful and frankly the world more successful, too,” Pompeo told Putin at the start of their meeting. “President Trump wants to do everything we can.”

On Iran, Venezuela and Russian interference in U.S. elections, Pompeo and Russian Foreign Minister Sergei Lavrov voiced sharp disagreement at a joint news conference. Still, Pompeo’s first trip to Russia as secretary of state represented a remarkable new attempt by the Trump administration to find fresh footing in its most politically treacherous international relationship. 

After several hours of talks between Pompeo and Lavrov — and another 90 minutes between Pompeo and Putin — Kremlin foreign policy adviser Yury Ushakov praised Pompeo for holding a “not bad, concrete conversation.” The United States had joined Russia in showing an interest, he said, in “starting to correct the relationship and gradually restoring communication channels.”

Trump has voiced a desire since his presidential campaign to cooperate with Russia on global challenges. But he never followed through on that desire with policy amid intense political head winds. 

Now, with the closure of the investigation by special counsel Robert S. Mueller III into Russian election interference, both the White House and the Kremlin see a new opportunity to reset ties. 

“For all of special counsel Mueller’s exotic work, he carried out an impartial investigation and confirmed the lack of any trace and any collusion between Russia and the acting administration — which we from the very beginning characterized as utter nonsense,” Putin told Pompeo at the start of their meeting. “This was one of the reasons for the worsening of our interstate ties. I hope that today, the situation is changing.” 

Pompeo said he had raised the issue of Russian election interference, but Putin again denied that it took place. 

“There are things that Russia can do to demonstrate that those kinds of activities are a thing of the past,” Pompeo said. If Russia were to interfere again in the 2020 U.S. election, Pompeo said, “it would put us in an even worse place.” 

With global tensions rising over Iran — a Russian ally — Lavrov said Russia was prepared to do what it could to avoid “a war scenario.” The United States has warned of an increasing threat from Iran and has dispatched additional forces to the region. 

“We fundamentally do not seek war with Iran,” Pompeo said. “We have also made clear to the Iranians that if American interests are attacked we will most certainly respond in the appropriate fashion.”

On Venezuela, Lavrov and Pompeo showed no sign of budging from opposing sides in that country’s crisis. But Pompeo also named regions where he saw potential for the United States and Russia to work together more closely. 

“Some of our cooperation has been excellent, on North Korea, on Afghanistan,” Pompeo told Putin. “We’ve done good work, counterterrorism work together. These are things we can build upon.”

In an apparent example of the Trump administration’s readiness to move past some points of disagreement, the biggest source of U.S.-Russian tensions during President Barack Obama’s tenure didn’t come up in Tuesdays’ talks, according to Kremlin aide Ushakov. 

“There was no Ukraine at all,” Ushakov said. 

Instead, Ushakov said, Putin and Pompeo discussed Syria, North Korea, Iran, Venezuela, and the New START accord.

A key test for Russia and the United States’ ability to cooperate will revolve around nuclear arms control. Pompeo said in the news conference that Trump remains interested in bringing other countries, including China, into an arms-control framework — an idea that has drawn skepticism in Moscow. 

In a striking bit of counterprogramming, Putin examined a new hypersonic, nuclear-capable missile system at a southern Russian defense plant before his meeting with Pompeo. The Kremlin insisted that the visit was coincidental. 

The United States backed out of a Cold War-era treaty with Russia limiting short- and medium-range ground-based missiles this year, citing Russian violations. 

Russian officials, meanwhile, have said they are eager to extend the New START accord, governing U.S. and Russian strategic nuclear weapons, which expires in 2021. Pompeo was noncommittal after his talks with Lavrov when asked whether the United States was prepared to extend the treaty.

“We will gather together teams that will work not only on New START and its potential extension but on a broader range of arms-control initiatives,” Pompeo said.

Pompeo’s trip comes amid a flurry of new talks between Moscow and Washington. Lavrov and Pompeo previously met in Finland earlier this month, and Trump and Putin recently spoke by phone for more than an hour.

“I had the impression that the president intends to rebuild U.S.-Russian relations and contacts in order to solve issues of mutual interest,” Putin told Pompeo, referring to the call with Trump. “We also would like to rebuild fully fledged relations and I hope that, right now, a conducive environment is being built for that.”

But Russia’s optimism remains guarded. Trump said Monday that he would meet Putin in person on the sidelines of the Group of 20 summit in Japan in June. Kremlin spokesman Dmitry Peskov, however, said Tuesday that a formal request from the White House for such a meeting has yet to arrive, and he noted that Trump canceled a meeting just before the two presidents were scheduled to meet in December. 

“We of course heard President Trump’s statement that he expects to hold a meeting with President Putin,” Lavrov said in the news conference. “If such a proposal officially arrives, then we will of course respond to it affirmatively.”

Some commentators and politicians in Moscow have voiced hope that with the end of the Mueller investigation, Trump may be in a better position to make good on his stated desire to improve relations with Russia. But others caution that even if Trump were to have more room to maneuver at home, the interests of the two countries continue to diverge around the world. 

“The domestic political atmosphere in the United States might seem to have become more favorable,” said Fyodor Lukyanov, a Russian international affairs analyst who has advised the Kremlin. “But in terms of foreign policy, things just keep getting worse.”