Brittney Griner is back in the US following 10 months in a Russian jail.

The White House is under pressure to free ex-US Marine Paul Whelan, who has been in a Russian jail for four years.

Russian President Vladimir Putin said more swaps were "possible" - a rare example of US-Russian co-operation amid Moscow's war with Ukraine.

When asked at a summit in Kyrgyzstan on Friday whether other US-Russia prisoner exchanges could take place, Mr Putin responded: "We aren't refusing to continue this work in the future."

He added that "everything is possible" and noted that "compromises" had been found to clear the way for Thursday's swap.

Griner, who was arrested in February for possessing cannabis oil at a Moscow airport, was traded for convicted weapons trafficker Viktor Bout, who was flown back to Russia after 12 years.

The American athlete was taken for evaluation to Brooke Army Medical Center in San Antonio, Texas, upon landing in the US on Friday.

It is unclear how long the Women's National Basketball Association (WNBA) star will remain at the facility.

The White House's John Kirby told US TV network MSNBC on Friday morning that the two-time Olympic gold medallist was in "good spirits" and "good health".

US President Joe Biden's administration has faced a backlash for not managing to bring home Whelan along with Griner.

The Michigan native was sentenced by a Russian court to 16 years in prison in 2018 on spying charges.

There will be "discussions going forward" on how to get Whelan back home, US state department spokesperson Ned Price said on Friday.

"Our message to him has been the same," he told MSNBC.

"We are coming for you. Keep the faith. We're going to bring you home just as soon as we can."

Whelan and his family have welcomed Griner's release, but the ex-Marine told CNN on Thursday by phone from the remote penal colony where he is being held that he was disappointed more had not been done to free him.

At the White House on Thursday, Mr Biden maintained efforts were continuing to bring Whelan home.

"While we have not yet succeeded in securing Paul's release we are not giving up," he said.

Republican lawmakers have led criticism of the White House, arguing that freeing such a high-profile prisoner as Bout should have warranted the release of two Americans.

Incoming House of Representatives Foreign Affairs Committee chairman Michael McCaul said the Biden administration "got played".

"We should be very careful, because if we don't negotiate these exchanges properly, it can end up in more detentions, false detentions of really innocent Americans in Russia," said the Texas Republican congressman.

Bout - known as the Merchant of Death - was serving a 25-year prison sentence in the US after his arrest in Thailand.

Since Griner's release, more details have emerged on US-Russia prisoner exchange negotiations.

This summer, Russia told the US it would be willing to swap Whelan for Vadim Krasikov, a former colonel from Russia's domestic spy organisation who is in German custody, according to a US official.

Moscow wanted a "spy for a spy", the official said.

The US appealed to the German government to try to include Krasikov - who was convicted of killing a Georgian citizen in Berlin in 2019 - but the country denied this request, the official said.

The US proposed several other options to the Russian government to try to secure Whelan's release, including Alexander Vinnik, a Russian citizen who is accused of money laundering, hacking and extortion, according to CNN. But those options failed, the outlet reported.

The swap is the second with Russia of Mr Biden's presidency. In April former US Marine Trevor Reed, who was convicted for attacking Russian officers during a drunken night in Moscow, was traded for convicted Russian drug smuggler Konstantin Yaroshenko.