The Obama administration is facing mounting pressure to use its leverage in the Iranian nuclear talks to demand the release of Americans imprisoned there -- as Tehran proceeds with charges critics say are unfair and unjust. 

The latest case involves Washington Post Tehran bureau chief Jason Rezaian, whom the newspaper revealed Monday is being charged by Iran with espionage and other alleged crimes. 

He had been arrested, along with his wife, in 2014. His wife was later released, but he has been detained at the notorious Evin Prison. The charges reported on Monday marked the first time they have been publicly described -- and the information only came from his lawyers, not from the court itself. A State Department official, asked Monday about the report, could not confirm the charges but said, if true, they are "patently absurd." 

"He should immediately be freed so he can return to his family. The charges should immediately be dismissed," spokeswoman Marie Harf said. 

White House Press Secretary Josh Earnest echoed those remarks at his daily briefing. Yet, when asked why the White House can't just tie the nuclear talks to the release of prisoners like Rezaian, Earnest said the talks are very "complicated" and must focus on one issue at a time. 

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The development comes after new details surfaced about the prison conditions endured by a former U.S. Marine held in Iran. It was the case of that ex-Marine -- Amir Hekmati, who was arrested in August 2011 on allegations of spying for the CIA while visiting his grandmother and other relatives in Iran -- that prompted the latest high-profile plea to the administration to link the talks to the prisoner issue. 

The Veterans of Foreign Wars on Friday called for Hekmati's release to be a part of the nuclear talks.   

"I am demanding that the U.S. government make his release a nonnegotiable part of whatever deal is cut with Iran," VFW National Commander John Stroud said in a statement. Stroud said he has "grave concerns" over Hekmati's imprisonment and allegations that "his Iranian captors are torturing a former Marine and a fellow VFW member." 

For weeks, administration officials have insisted that the Iran nuclear talks will not involve non-nuclear issues. The State Department said as much when Israeli leader Benjamin Netanyahu urged negotiators to enshrine Israel's "right to exist" in any agreement. 

"This is an agreement that doesn't deal with any other issues, nor should it," Harf said at the time. 

But last week, President Obama showed a willingness to compromise regarding Congress' demands that it be allowed to review any potential nuclear agreement. 

Some want the administration to budge, as well, on the prisoner issue. 

"There's a lot wrong with negotiating a deal with Iran, but the ongoing nuclear talks -- love them or hate them -- are probably the only chance for the Administration to ask for the return of Amir Hekmati and others," Rep. Duncan Hunter, R-Calif., said in a statement. "Frankly, it should have happened already, ahead of reaching just the framework, but with each day and concession, the Administration loses its leverage and influence." 

Stroud cited last year's controversial swap of five Taliban militants for Sgt. Bowe Bergdahl, who has since been formally accused of desertion. 

"If our government can swap five of the worst terrorists for one American soldier, we can certainly make the safe release of one former Marine an unconditional part of a deal that has yet been formalized," Stroud said. 

Rezaian and Hekmati are being held in Iran, along with Christian pastor Saeed Abedini. 

Further, Robert Levinson, an American private investigator and former FBI agent, disappeared in Iran in 2007, and some believe he's being held inside the country, though Tehran denies it has him. 

Supporters of the first three have pushed the U.S. to make securing their freedom part of a deal that could see the West drop international sanctions against Iran in exchange for assurances the hardline Islamist nation will significantly curb its nuclear program. 

Iran's commitment to the recently unveiled framework, though, is in doubt. Leaders have pushed for immediate sanctions relief, though the Obama administration claims that would be conditional. And now, a senior Iranian military leader has vowed that nuclear inspectors would not be allowed on military sites, though the Obama administration fact sheet said the deal would allow inspectors access to "suspicious sites." 

All sides are trying to reach a final deal by June 30. 

The talks with Iran, as well as talks with Cuba -- which continues to harbor U.S. fugitives -- have raised concerns from Capitol Hill and beyond, and prompted the calls for the administration to demand more from the other side of the table. 

"It is critical that our government use this unique opportunity -- as our two nations continue to sit at the negotiating table over the next few weeks and months -- to bring Pastor Saeed and the other wrongfully imprisoned Americans home to their families," Jordan Sekulow, executive director of the American Center for Law and Justice said earlier this month, after Obama announced the framework for an agreement had been reached.  

Obama recently stressed the importance of their release. On March 20, at the start of the Persian New Year, Nowruz, Obama said: "At this time of renewal, compassion, and understanding, I reiterate my commitment to bringing our citizens home and call on the government of the Islamic Republic of Iran to immediately release Saeed Abedini, Amir Hekmati and Jason Rezaian and to work cooperatively with us to find Robert Levinson so that they all can be safely reunited with their families as soon as possible." 

Secretary of State John Kerry also said recently that negotiations to release the Americans are continuing. "I'm not going to go into any details except to say to you that that conversation is continuing," Kerry said. "We have a very specific process in place to try to deal with it, and we call on Iran again, today, now, in light of this, to release these Americans and let them get home with their families. And we are working on that and we will continue to be very focused on it." 

In interviews with Fox News, Hekmati's family members have described a dire situation for the imprisoned American. 

Last week, Hekmati's sister and brother-in-law appeared on Fox News Channel's "On the Record with Greta Van Susteren," where they described in chilling detail the torture that the veteran has endured since his arrest in August 2011. 

Hekmati, they said, has suffered stun-gun assaults, has been whipped, dosed with lithium and hung by his arms while held in the Islamic Republic. 

"He was drugged with lithium for a long period of time and then forcibly it was removed so that he would have to endure painful withdrawal symptoms and then he was whipped on his feet," his sister Sarah said. 

But Richard Grenell, former U.S. spokesman for the U.N. under the George W. Bush administration, told Fox News that the department is right not to tie the prisoner issue to the nuclear talks. 

"They need to separate these issues. We don't want to encourage another country or another entity or another group to actually take Americans and then sit down across the table and, you know, use those Americans as negotiating chips. We absolutely want to discourage that," Grenell said. 

FoxNews.com's Perry Chiaramonte contributed to this report.