Supporters of Iraqi Shiite cleric Moqtada al-Sadr gather during a protest. AFP
The populist cleric's announcement came amid behind the scenes talks aimed at steering Iraq out of crisis, with the country's two branches of Shiite Islam jockeying for supremacy.
More than 10 months on from elections, Iraq still has no government, new prime minister or new president, because of disagreement between factions over forming a coalition.
Sadr wants parliament dissolved to pave the way for new legislative elections, but his rivals the pro-Iran Coordination Framework want to set conditions and are demanding a transitional government before new polls.
The cleric's bloc emerged from last October's elections as parliament's biggest, but still far short of a majority.
Sadr, whose supporters have been staging a sit-in protest outside parliament in Baghdad's high security Green Zone for more than two weeks, had called for a "million-man demonstration" in the capital on Saturday.
But on Tuesday he announced on Twitter "the indefinite postponement of Saturday's protest".
"If you had been betting on a civil war, I am betting on preserving social peace. The blood of Iraqis is more precious than anything else," Sadr said.
Late on Monday, a committee organising demonstrations in support of the Coordination Framework also announced new gatherings, but without setting a date.
The Coordination Framework launched their own Baghdad sit-in on Friday, camping out on an avenue in the capital.
The Coordination Framework comprises former paramilitaries of the Tehran-backed Hashed al-Shaabi network and the party of former premier Nuri al-Maliki, a longtime Sadr foe.
So far the rival Shiite protests have been peaceful, with attempts at mediation ongoing.
Hadi al-Ameri, leader of a Hashed faction, has also called for calm and for dialogue. He has had a series of meetings with political leaders including allies of Sadr.
Also on Tuesday, Finance Minister Ali Allawi who is in the current government submitted his resignation to the Council of Ministers, the INA state news agency reported.
Iraq has been ravaged by decades of conflict and endemic corruption.
It is blighted by ailing infrastructure, power cuts and crumbling public services, and now also faces water shortages as drought ravages swathes of the country.
Despite its oil wealth, many Iraqis are mired in poverty, and some 35 percent of young people are unemployed, according to the United Nations.