"There is tangible progress," he told AFP in a phone interview from Damascus, where the Palestinian group's exiled leadership is based. He gave no further details.
Both Hamas and Israel have been secretive about the details of the exchange, which have dragged on after Palestinian fighters captured Israeli soldier Gilad Shalit in a cross-border raid from Gaza in 2006.
Hamas is demanding freedom for hundreds of prisoners in return, including about 450 terrorists serving life sentences or long prison terms after they were convicted of attacks against Israelis.
Both Israel and Hamas reported progress in the talks earlier this week but have since downplayed reports of an imminent deal.
A senior delegation from Hamas in the Gaza Strip met a German mediator in Cairo earlier this week and then headed to Damascus to consult with the Islamist group's leadership before returning to Gaza on Thursday.
A Hamas official said the talks will be suspended until the end of the Muslim Eid al-Adha holiday on Tuesday, but officials close to the negotiations said contacts with mediators would continue.
Egypt and more recently Germany have been brokering the indirect negotiations.
'Not at any price'
One official, who requested anonymity because of the sensitivity of the talks, said there had been progress over some prisoners Israel initially refused to release, but Israel turned down other inmates Hamas demanded.
He said there were more than several prisoners under dispute.
A senior Hamas leader in Gaza said Israel was stalling the talks by not "answering the demands of Palestinian factions."
Defense Minister Ehud Barak said on Thursday that the Jewish state wished to strike a deal with Hamas "but not at any price."
Shalit is to be handed over to Egypt before Israel frees the first group of hardcore prisoners, and then returned to Israel, after which hundreds more prisoners will be freed.
But Abu Marzouk said the prisoner exchange deal was not linked to a truce, which would allow much-needed goods and reconstruction material into Gaza, an impoverished enclave that was devastated by a 22-day war at the start of 2009.
Israel and Egypt have maintained a partial blockade of the territory since Hamas took it over in 2007.