The four-member Bjorn Again band said it traveled 200 miles north of Moscow for the Jan. 22 gig on the shores of Lake Valdai to perform before an exclusive audience of eight people - Putin, an unidentified blonde woman and six other men in tuxedoes.
Putin's spokesman denied that the prime minister attended any such concert, but band members gave plenty of details and said they recognized Putin at the show.
ABBA was one of the best-loved foreign bands during Soviet times, and the Swedish quartet even traveled to Moscow to perform in the Kremlin.
But revelations that Putin could be a closet ABBA fan run counter to his traditional strongman image. The prime minister is better known for manly displays on the judo mat and in fighter jet cockpits, and for robust outbursts against the West.
Rod Stephen, founder of Bjorn Again, originally thought it was a hoax when he received a phone call requesting that his band travel to to perform at Lake Valdai.
"It was the classic 'hello ... Kremlin ... Russia ... we want Bjorn Again'," recalled Stephen. "I thought it was one of the band members sending me up."
But they soon understood the offer was serious.
Aileen McLaughlin, one of the four band members who traveled to Russia, said the group found the whole experience "bizarre" from the start. After flying into Moscow, they boarded a bus for a nine-hour journey on "very bad" roads and learned they were to perform before Putin.
"We arrived at 5 in the morning at big metal security gates, where we had to get out and be searched," she said by telephone from London. "We were just tired and wanted to get to the hotel. Oh my - were we wrong again!"
McLaughlin said they stayed in a place resembling a military installation, with very basic accommodations and tight security. The band members were guarded by machine gun-toting security guards and cameras, and when any of them ventured outside, they were prevented from straying by men with Kalishnikovs.
But she said the audience - comfortably seated on three sofas - appeared to enjoy the concert.
"They were clapping and swaying, and putting their fingers in the air, that kind of thing," said McLaughlin. "He (Putin) had good rhythm. He was shouting 'Bravo, Bravo!' after the songs."
The audience particularly enjoyed "Super Trouper" and "Mamma Mia," she added.
A lace curtain separated the band from the elite audience for the hour-long, high-security show, but McLaughlin said at one point the spotlight flashed on the audience and band members saw Putin.
McLaughlin described the lone woman as a blonde who was "wearing a long, cream, really pretty dress." Putin's wife, Lyudmila, has blond hair, but they are rarely seen together anymore.
The band was paid 20,000 pounds($30,000) for their performance, which was organized by the Moscow-based agents SAV Entertainment, said Stephen, speaking from London.
A woman at SAV Entertainment denied that the company had anything to do with the event.
"We are telling everyone that such a concert never took place. We are denying it," she said, refusing to give her name.
Putin spokesman Dmitry Peskov denied that Putin attended any such party on or around Jan. 22, adding "neither Mr. Putin nor his apparatus ordered any band of this kind."
"I have no doubt that he likes some music of Abba," Peskov said. "But he simply wasn't there."