Iranian authorities have granted a four-day leave on humanitarian grounds to Baquer Namazi, the oldest of a group of American citizens known to be held in the country.
Mr Namazi's lawyer, Jared Genser, said the 81-year-old former Unicef official cannot leave Iran and is prohibited from speaking to the media. His son, business consultant Siamak Namazi, is still in jail.
Both are dual Iranian-American citizens.
Mr Namazi was rushed to a hospital on January 15 — the fourth time in the last year — after a "severe" drop in his blood pressure, an irregular heartbeat, "serious" energy depletion and white colouring, Mr Genser said.
In September, he underwent emergency heart surgery to install a pacemaker.
"We welcome the release of Baquer Namazi given his deteriorating health, but we note that his release is only temporary," said US state department spokeswoman Heather Nauert.
"We call for the immediate and full release of the Namazi family, including his son, Siamak, as well as other Americans unjustly held by the Iranian government."
The Namazis were given 10 years in prison for "espionage and collaboration with the American government" in October.
Baquer Namazi was given his four-day leave on Sunday. His son Babak said "a return to prison would be life-threatening for him".
"I beg the Iranian authorities to show compassion and grant my father a permanent release so he can spend his remaining time with his family before we face an irreversible tragedy," he added.
Mr Genser said returning to prison on Thursday as ordered would amount to a "death sentence" for Mr Namazi.
"On humanitarian grounds, his leave must be made permanent. And it is urgent that Siamak Namazi and the rest of the wrongfully imprisoned Americans also have their cases resolved," Mr Genser said.
Xiyue Wang, a Chinese-American researcher from Princeton University, was also given a 10-year sentence for espionage.
Ex-FBI agent and CIA contractor Robert Levinson went missing in March 2007.
Washington and Tehran have had no diplomatic relations since April 1980 in the wake of the Islamic revolution, and tensions have sharpened under president Donald Trump after a brief warming under his predecessor, Barack Obama.
The two countries along with other major powers signed an accord on July 14, 2015 aimed at curbing Iran's nuclear programme. Washington has continued to honour the accord, despite Mr Trump's threats as a candidate last year to "rip it up".