Yatsina was abducted while on assignment in the troubled North Caucasus republic in the summer of 1999, and murdered on February 20, 2000.
"Responding to a request from the Swedish justice ministry, the Russian General Prosecutor's Office has sent it additional evidence necessary for the extradition of Mahomed Uspaev, who was detained there in August," the statement said.
Uspaev, who claims to be a cousin of the late Chechen militant leader Aslan Maskhadov, killed by Russian Special Forces in March 2005, arrived in Sweden in 2002 and received a residency permit in 2004.
The Prosecutor's Office said that Uspaev acted out of extremist convictions when he abducted the Russian journalist on July 19, 1999, and later killed him.
Uspaev's attorney, Richard Backenroth, said that while his client does not deny having participated in the Chechen conflict, he denies abducting and killing Yatsina.
The Swedish justice ministry is reviewing the extradition request.