They gave no further details about the body.
"That is a blatant lie," said Dariya Dorokhina, one of the activists.
The rally is part of a series of 'dissenters marches' held by the Other Russia coalition, which is led by Garry Kasparov, in protest against government policies.
Kasparov withdrew his presidential candidacy in December 2007 following what he said was government pressure.
The rallies are rarely sanctioned and frequently broken up by riot police.
Dorokhina said the police "blockade" was a continuation of tactics employed before previous opposition rallies, when police waiting outside individuals' apartments would detain them when they stepped outside.
The activists aimed to avoid such a detention by renting an apartment for the day as a gathering place.
"They just followed us all the way to this apartment," Dorokhina said.
The activists met at the apartment on Tuesday morning and told police who arrived an hour later that they would not open the door because they had committed no crime, Dorokhina said.
Yevgeny Gildeyev, a spokesman for Moscow police, accused the activists of "provoking" police.
"A group of young people waiting in the courtyard ran inside the house when they saw police officers approach," Gildeyev said.
"In line with normal procedures, police officers wanted to speak to all possible witnesses," he said.
As the standoff went into the late afternoon, the activists unfurled a banner reading 'freedom' several times from a window of the apartment on the top floor of the nine-storey building.
Also on Tuesday, police detained 12 members of the opposition group 'Left Front' who were blockading the entrance to the information centre of the United Russia party, the political organisation of which Putin and Medvedev are members.