Wasif 's brother, speaking from the northern Lebanese city of Tripoli, said his family had received word Hassoun was alive and had been released in the early hours of Tuesday, but declined to specify the source of the information.
"We got solid assurances that my brother is alive and was released today," he told reporters.
There has been confusion in the last several days about Hassoun's fate, with statements on web sites saying he had been decapitated, then that he was still alive.
The US military had confirmed that Hassoun went missing from his unit.
A statement delivered to Aljazeera, a purported Iraqi resistance group has said it has sent a US marine, who had earlier been reported killed, to "a safe place".
The Islamic Response Movement said that Hassoun had been moved to "safety" after pledging to leave the military.
Hassoun's family in Lebanon had appealed to his captors to have mercy on him as an Arab and a Muslim, and called on an Iraqi religious group which has negotiated the release of hostages seized by Islamists in Iraq to help free him.
"We got solid assurances that my brother is alive and was released today"
Sami Ali Hassoun
The group, calling itself Islamic Response - the Security Wing of the Islamic Resistance of Iraq, said on Monday it sent Cpl Wasif Ali Hassoun, a US marine of Lebanese heritage, to a "safe place" but without specifying the exact location.
The armed group said Hassoun announced he will not rejoin the US army.
The US marines said they had no news of Hassoun's release and were still listing him as captured. "We're not going to comment on what Aljazeera is saying," said Lieutenant Corporal TV Johnson.
"When we have more information on his status, which is proven, we'll release it," he said.
Aljazeera broadcast a videotape on 27 June showing Hassoun kneeling blindfolded as a curved sword loomed overhead.
An audio statement from armed fighters threatening to kill him unless the US released all Iraqis in "occupation jails" accompanied the video portion of the tape.
On Sunday, a group calling itself the Army of Ansar al-Sunna denied reports published on websites that said it had decapitated Hassoun.
The group who captured the marine
denied reports of him being beheaded
"The denial gave us a big relief," Hassoun's brother, Sami, said by telephone from the northern Lebanese city of Tripoli, where he, his father and several other relatives live.
Other armed groups have captured and threatened to behead foreign Muslims working for the US in Iraq, creating an uproar among many Muslims, including other armed fighters.
All the captured Muslims have been released unharmed.