US Secretary of State Mike Pompeo is heading to Russia with an unusual and thankless task — standing firm against the rival power even as his boss, President Donald Trump, reaches out to reconcile.

Pompeo will meet with Putin on Tuesday in the Black Sea resort of Sochi, in the highest-level US engagement with the Russian leader since a July summit in Helsinki after which Trump faced wide scorn at home for his trustful embrace of the Russian leader.

The top US diplomat's trip comes less than two months after Special Counsel Robert Mueller wound up an investigation that found that Russia interfered in the 2016 presidential election — but that the Trump campaign did not collude with Moscow.

After spending the first two years of his presidency under the cloud of Mueller's probe, Trump chatted for more than an hour by telephone with Putin on May 3, in what he hailed as a "very positive" conversation.

Trump said that Putin had assured him that Russia was not involved in Venezuela — directly contradicting Pompeo and other top officials who for weeks have demanded that Moscow stop backing leftist leader Nicolas Maduro, whom Washington is trying to topple.

Venezuela is only one of a slew of issues where the United States and Russia have clashed.

Others include the Syrian war, arms control commitments and the conflict in Ukraine, where Western powers have been attempting for five years to little avail to end Moscow's support for armed separatists.

Jonathan Katz, a former US official focused on Central and Eastern Europe, believed that Russia was looking to see if the end of Mueller's probe would allow a new beginning with Trump, whom Putin supported over Hillary Clinton in 2016.

"I think this is Moscow testing whether there is a new modus operandi in Washington, (after) the release of the Mueller report," said Katz, now a senior fellow at The German Marshall Fund of the United States.

Despite heading the US government, Trump is a major outlier in Washington, with virtually all senior administration officials including Pompeo and lawmakers across party lines advocating a harder stance on Russia, including sanctions over election interference and its 2014 takeover of Crimea from Ukraine.

For Pompeo, "it's incredibly difficult because the interlocutors on the other side don't know who speaks for the United States," Katz said.

Progress sought on arms control

A State Department official said Pompeo, who will also meet with Russian Foreign Minister Sergei Lavrov for the second time in as many weeks, would push for progress in particular in one area — arms control.

The New START treaty, which caps the number of nuclear warheads well below Cold War limits, is set to expire in 2021 and Trump has called for a broader successor that will include a rising China.

Even Pompeo has acknowledged that those goals may be too optimistic.

Another key accord, the Intermediate-Range Nuclear Forces treaty, just collapsed, with the United States pulling out over charges that a new Russian missile system violated it.

Despite deep rifts on many hotspots, the State Department official said that Russia and the United States, if not seeing eye-to-eye, had developed "constructive" relationships on Afghanistan and North Korea.

"It is in our interest to have a better relationship with Russia," the official told reporters on condition of anonymity.

"Where we have concerns, we're going to raise them directly, narrow those differences and find areas where we can cooperate to protect and advance our interests."

But Victoria Nuland, who championed a tough line on Russia as an assistant secretary of state during Barack Obama's administration, voiced doubt on whether hopes for a better relationship could be realised under Putin's increasingly autocratic rule.

She said that a "lack of leadership, unity and consistency" in the United States was the greatest challenge to countering a resurgent Russia.

"What we don't know, and what we have to continue to test, is whether Russian President Putin truly wants to improve relations," she recently testified before the House Foreign Affairs Committee.

"It may well be that his psychology and leadership model are too dependent on an enemy abroad to change course — and we have to steel ourselves for what may be a very long game that outlasts Putin."