The Obama administration’s ability to secure the freedom of two Americans from Yemeni captors is evidence of White House indifference to a man they left behind, attorneys for a third US citizen trapped in the “nightmarish” country have said.

Sharif Mobley, the 32-year-old American imprisoned since 2010, was not one of the two as-yet-unnamed American hostages released by Houthi rebels in Yemen.

But after the White House welcomed word of their release on Sunday, Mobley’s lawyers argued the latest hostage release showed that had the US actually sought to free their client, diplomats could pull off such a deal.

They also confront a macabre possibility: that Mobley’s life is in danger, either inside his cell on a military base in the Yemeni capital of Sana’a, or from airstrikes launched by US allies in the Saudi-led coalition to roll back January’s Houthi coup.

The White House said on Sunday that it had been “in regular contact” with the families and representatives of the freed hostages. “We have worked tirelessly to secure their release,” a National Security Council spokesman, Ned Price, said in a statement.

Cori Crider, a lawyer with the human-rights group Reprieve, which represents Mobley, called the releases “yet more proof that where there is a political will, there is a practical way to get US men released from captivity in Yemen”.

“The US know where Sharif is, and they are helping the Saudis to bomb the country to pieces,” Crider said. “Yet they won’t ensure his safety or get him out of there – they won’t even respond to his family’s requests for help.”

Mobley’s family and representatives have been stonewalled by US State Department officials, correspondence shared with the Guardian shows.

“It is deeply regrettable that we have had no substantive communications from you in this regard,” Kat Craig, Reprieve’s legal director, wrote to State Department official William Lesh in May, after “repeatedly” imploring the department to urge Saudi Arabia to spare Mobley.

On 14 May, Mobley told his horrified sister via a smuggled cellphone: “They’re trying to kill me here at the prison.”

Mobley’s captors have beaten him and made him drink water from a bottle once filled with urine, he has said on the calls. But he faces another danger from outside his jail in Sana’a: Saudi warplanes that have bombed the military base where he is imprisoned, which hosts an anti-aircraft battery.

Mobley’s lawyers say he is still alive as of last week, when Mobley was able to call his sister after months of silence.

In 2010, Mobley, an American studying in Yemen whose friends have said was developing extremist views, was snatched off the streets at gunpoint by masked men and shot in the leg. He awoke in Yemeni custody in a hospital bed and confronted by interrogators who identified themselves as “Matt from FBI and Khan from DOD [the Department of Defense]” and wanted to know about terrorism.

Yemen dropped terrorism accusations against Mobley but charged him with the murder of a guard from an alleged escape attempt. His case never proceeded to trial, however, as in February 2014, Mobley’s lawyers lost contact with him in the warrens of the central prison in Sana’a. He emerged via phone in military prison shortly before the Iran-supported Houthi movement overthrew the US-backed Yemeni government.

The White House did not reply to a request for comment about Mobley. The State Department, since the spring of 2014, has denied requests for information about Mobley on the grounds that doing so would violate his privacy. It has yet to fulfill a Freedom of Information Act request about its involvement in Mobley’s case.

A State Department statement provided to the Guardian on Monday was almost identical to one provided on 4 June:

“The safety and welfare of US citizens overseas is among our top priorities. Consular officers strive to assist US citizens detained abroad whenever possible. On February 11, 2015, due to the deteriorating security situation in Sana’a, the Department of State suspended all embassy operations and US Embassy Sana’a American staff was relocated out of the country. All consular services in Sana’a have been suspended until further notice. Due to privacy considerations, we are unable to provide further information.”

The two US citizens the Obama administration worked to free follow the release of a similarly detained American, journalist Casey Coombs, in June. “Just save his life,” Mobley’s sister, Caamilya Beyah, begged US officials, to no substantive reply.

Crider, of Reprieve, said: “Given the nightmarish situation in Yemen, the State Department really ought to be doing for Sharif what it’s done for these others, and see that he’s evacuated from the war zone as soon as possible.”