Several Iranian-Americans held in US prisons after being charged or convicted for sanctions violations have been released, their lawyers told Reuters on Sunday, as part of a deal between Iran and the US that also won the release of four Americans imprisoned in Iran.

Earlier, a Swiss plane carrying four American prisoners and some family members left Tehran as part of the prisoner swap deal. The four are Jason Rezaian, the Washington Post's Tehran bureau chief; Saeed Abedini, a pastor from Idaho; Amir Hekmati, a former Marine from Flint, Michigan; and Nosratollah Khosravi-Roodsari. A fifth prisoner, the American student Matthew Trevithick, was released separately from the other four on Saturday, a US official said.

The United States said on Saturday that it had granted clemency to seven Iranians being held in US jails or awaiting trial, mostly on sanctions-related charges. Six of the men are Iranian-American dual citizens.

Bahram Mechanic and Khosrow Afghahi were released from a Houston jail early on Sunday, Mechanic's lawyer Joel Androphy said.

"Releasing Khosrow Afghahi is the correct result," said Afghahi's attorney, David Gerger, in an emailed statement. "He is a good man, and we are happy to put this ordeal behind him."

Tooraj Faridi, also granted a pardon in connection with the case against Mechanic and Afghahi, was already out on bail.

Arash Ghahreman, convicted in 2015 of trying to export US-built marine navigation equipment to Iran, was also released, his attorney Ellis Johnston said on Sunday.

A lawyer for Ali Saboonchi, convicted in 2014 for export violations, said his client had also been released as of Sunday.

"Ali is thrilled and grateful for his release and return to his family," said his attorney Lucius Outlaw, a federal public attorney, in an emailed statement. "Ali's release shows that he poses no danger to the American people."  -Reuters