The United States wants an explanation for why Russia detained a retired US Marine on spying charges in Moscow and will demand his immediate return if it determines his detention is inappropriate, Secretary of State Mike Pompeo said on Wednesday.

US Ambassador to Russia Jon Huntsman visited Paul Whelan at a detention facility in Moscow and spoke by phone with his family, the State Department said.

The United States had expressed concern through diplomatic channels over delayed access to Whelan, who was detained on Friday, a department spokesman said in a statement.

Secretary of State Mike Pompeo said on Wednesday that if the detention of the former Marine "is not appropriate, we will demand his immediate return".

In announcing Whelan's arrest three days after he was detained, the Russian Federal Security Service said he was caught "during an espionage operation", but gave no details.

Whelan, 48, was in Moscow to attend a wedding when he suddenly disappeared, his brother David Whelan said on Tuesday.

Pompeo, speaking in Brazil, said the US had "made clear to the Russians our expectation that we will learn more about the charges and come to understand what it is he's been accused of and, if the detention is not appropriate, we will demand his immediate return."

Whelan's family said in a statement David Whelan posted on Twitter: "We are deeply concerned for (Paul's) safety and well-being. His innocence is undoubted and we trust that his rights will be respected."

The Russian spying charges carry a prison sentence of up to 20 years.

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David Whelan said in an interview that his brother had been to Russia several times previously, so when a fellow former Marine was planning to marry a Russian woman in Moscow he was asked to go along to help out.

The morning of his arrest, he had taken a group of wedding guests on a tour of the Kremlin museums. The last time anyone heard from him was at about 5pm local time, and he failed to show up that evening for the wedding, his brother said.

"It was extraordinarily out of character," he said.

Strained relations

The State Department said on Monday it had received formal notification from the Russian Foreign Ministry of the arrest. David Whelan said the family was told by the US Embassy in Moscow that they had not been able to speak to his brother.

David Whelan said he has no idea why his brother was targeted by the Russian security services.

"I don't think there's any chance that he's a spy," David Whelan told CNN on Wednesday.

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Paul Whelan did multiple tours in Iraq with the Marine Corps, his brother said. He now lives in Novi, Michigan, and is director of global security for BorgWarner, where he has worked since early 2017.

The arrest comes as US-Russian ties are severely strained, in part over an investigation into Russian meddling in the 2016 presidential election.

A Russian gun rights activist, Maria Butina, is in US custody after admitting she acted as a secret agent for the Kremlin in trying to infiltrate conservative US political groups as Donald Trump was seeking the presidency. She pleaded guilty in December to a conspiracy charge as part of a deal with federal prosecutors.

Russian President Vladimir Putin has claimed that the case is fabricated and that Butina entered the guilty plea because of the threat of a long prison sentence