He said the talks would be held directly, without intermediaries, the Reuters news agency reported, citing Russia's RIA Novosti.
On Thursday, the United States freed Russian arms dealer Viktor Bout in exchange for American basketball star Brittney Griner, who had been imprisoned in Russia, according to news outlets.
The swap was a rare instance of cooperation between Washington and Moscow since Russia's invasion of Ukraine in early February, Reuters reported.
It noted that Russia in April released former US Marine Trevor Reed and the United States freed Russian pilot Konstantin Yaroshenko.
Griner, a two-time Olympic gold medalist and star of the Women's National Basketball Association's Phoenix Mercury, landed in the United States early on Friday after 10 months in Russian detention, according to Reuters.
Announcing her release on Thursday, US President Joe Biden said the swap ended months of "hell" for her and her wife, Cherelle Griner.
Brittney Griner was detained on February 17 after vape cartridges containing cannabis oil, which is banned in Russia, were found in her luggage at a Moscow airport, Reuters reported.
Meanwhile, Biden said his administration remained committed to also securing the release of imprisoned former Marine Paul Whelan from Russia, according to Reuters.
(gs)
Source: Reuters, IAR, PAP