Mr McCain has been an outspoken critic of Russia
The Russian mission to the UN in New York says it has turned down a request from John McCain to help fund his presidential campaign.
Ambassador to the UN Vitaly Churkin and others received standard mail-outs asking them to help "stop the Democrats from seizing control of Washington".
Spokesmen for the McCain campaign and the mission accepted the letters were "a computer error".
Mr McCain has been a strong opponent of Russia on human rights and Georgia.
Brian Rogers, a spokesman for the McCain campaign, told the BBC the campaign had not itself received any complaints from the mission and that "it sounds like they're having a little fun at our expense".
"It's just an error," he said.
US presidential candidates are legally barred from accepting foreign donations.
The letter to Mr Churkin has a return form which carries the words: "I am proud to stand with our Republican candidates as the Obama Democrats and their wealthy liberal backers focus their attacks squarely on defeating Republicans and gaining control of our government.
"I want to do all I can to help stop the Democrats from seizing control of Washington and implementing their radically liberal policy for our nation."
The form then has a space for a signature over the typed name, Vitaly Churkin.
On the copy the Russians released, the space is unsigned.
Ruslan Bakhtin, a spokesman for Russia's UN mission, said: "It's evident that [the letter] was a mistake. It happens."
But he also stressed: "Russian authorities are in no way engaged in funding political campaigns or political activities abroad."
Mr McCain has opposed Moscow on a number of measures.
To evade Russia's veto in the UN Security Council he has proposed setting up an alternative body: the League of Democracies.
During the Russia-Georgia conflict this summer, he said: "We are all Georgians now."
He has also proposed throwing Russia out of the G8 over its human rights record.