Barghouti is the most popular leader in the Palestinian territories, and is widely regarded as the only figure able to unify clashing Palestinian factions, rein in militants and get peacemaking with Israel moving again.
"If we want to blunt Hamas's capabilities ... and if we ultimately want a civil rather than a religious government like those taking shape across the Arab world, we have to make a contribution," Ezra told Army Radio, in defence of freeing Barghouti.
"I think it could definitely help Abu Mazen [Abbas]."
Abbas and his Fatah loyalists are engaged in an increasingly deadly power struggle with the ruling Hamas faction, which rejects Israel's right to exist and unseated Fatah in elections last year.
The infighting has weakened Abbas as he tries to relaunch long-stalled peace talks with Israel, which considers him a legitimate negotiating alternative to Hamas.
Miri Eisin, Ehud Olmert's spokeswoman, said the release of Barghouti - who is serving five life sentences for the murders of four Israelis and a Greek monk - was "not on the agenda".
But Ezra, a member of Olmert's Kadima party, said Israel has freed "much worse murderers" in the past.
Several weeks ago, the deputy defence minister, Ephraim Sneh of the Labour party, also championed Barghouti's release.