Brittney Griner, the American basketball star who has been released from almost 10 months of detention in Russia in a prisoner swap with the notorious arms dealer Viktor Bout, is undergoing physical and mental evaluation at a Texas army facility as part of her rehabilitation to the US.

The two-time Olympic gold medalist is being debriefed at the Brooke Army Medical Center in San Antonio. She arrived back in the US on Friday morning and was immediately taken for what was being described as “extensive health evaluations”.

The national security council’s strategic communications coordinator, John Kirby, told This Week on ABC News on Sunday that early indications were that Griner was doing well. “She’s in very good spirits and in good health,” he said.

As the WNBA and Olympic champion gradually re-enters US society, the political fallout over her high-profile prisoner exchange with Bout continued. So too did the ongoing plight of other Americans held by Russia not included in the Kremlin deal, notably the discharged marine Paul Whelan who has served almost four years of a 16-year sentence for alleged spying.

Joe Biden’s special presidential envoy for hostage affairs, Roger Carstens, said that negotiations over Whelan were continuing. He told CNN’s State of the Union: “We have an ongoing open dialogue with the Russians and we have the commitment of the president, and my office certainly, to bring Paul Whelan home.”

Carstens described speaking with Whelan in a Russian prison a day after the swap securing Griner’s release was announced and assured him that the US government was committed to bringing him home. He said he urged Whelan to “keep the faith – we’re coming to get you”.

The White House has responded to criticism that they should have secured the release of both Griner and Whelan in exchange for such a prominent arms dealer by insisting that a two-for-one deal was never on the cards. Carstens said a specific proposal to get both individuals out had been made to the Russians but “it didn’t land anywhere”.

He added: “It was clear that they were treating Paul very separately because of these sham espionage charges they levied against him.”

The Biden administration also continues to come under fire from Republican critics and others for letting an infamous arms dealer go free. Bout, nicknamed the “merchant of death”, was sentenced to 25 years in prison for conspiracy to kill Americans and for selling weapons to FARC insurgents in Colombia.

The Democratic senator from New Jersey and chair of the foreign relations committee, Bob Menendez, has denounced Bout’s release as “deeply disturbing”. He said it would embolden dictators to take hostages.

“We must stop inviting dictatorial and rogue regimes to use Americans overseas as bargaining chips,” he said.

Top Republicans have been using similar arguments to attack Biden. The former secretary of state under Donald Trump, Mike Pompeo, told Fox News Sunday that Vladimir Putin and other hostile regimes including Iran would be encouraged.

“Trade bad guys for celebrities creates the wrong incentives for the bad guys,” he said.

In his CNN interview, Carstens acknowledged that the decision to cut a deal with Russia had been difficult. “It’s hard to keep these dictators and dictatorial governments from taking Americans and trying to use them as bargaining chips,” he said, adding that Biden had introduced new sanctions against people taking hostages abroad that he promised would be rolled out soon.

Carstens also gave new details of how he had met Griner as part of the prisoner swap in Abu Dhabi and then escorted her back to the US. On the 18-hour flight, she had spent about 12 hours just talking, including about her Russian ordeal.

“I was left with the impression this is an intelligent, passionate, compassionate, humble, interesting person – a patriotic person,” the envoy said.

Griner was sentenced to 9.5 years in prison after she was arrested at an airport in Russia and accused of carrying vape canisters with cannabis oil in them. The basketball star said she had made a mistake in packing the canisters and presented evidence that she had been prescribed the cannabis as a pain treatment.

Bout told RT television, the Russian state-run network, that he had exchanged words with Griner on the tarmac in Abu Dhabi. “I wished her good luck, she even extended her hand,” he said, according to a report in the Washington Post.

Bout was asked by RT whether Griner had engaged with him. “Yes she did, and I felt she was very positive towards me,” he said.

The claim cannot be independently verified. Griner has not commented, and edited video footage released by Russian state media appears to have been cut at precisely the moment that any direct encounter between the two individuals would have taken place.