Will not enter the coalition and the movement "For the rule of law", headed by former Prime Minister Nuri al-Maliki.
After the election results were announced, he said he would only cooperate with Prime Minister Haider Al-Abadi, with the Kurds and the Sunnis.
On Tuesday, the prime minister called Sadr to congratulate him for the election victory, the cleric's office said.
Victory for the veteran nationalist's Marching Towards Reform alliance with Iraq's communists - pitched as an anti-corruption outsider force - would be a slap in the face for Iraq's widely reviled ruling establishment.
Voter turnout was at a low 44 percent, 15 percent lower than the turnout in the 2014 parliamentary elections.
American diplomat, involved in fatal traffic accident, allowed to leave Pakistan
The United States and Pakistan imposed travel restrictions on each other's diplomats last week as the dispute continued to simmer. On April 24, the federal government informed the IHC that name of the United States diplomat had been placed on the blacklist.
Abadi, who is the preferred candidate of the United States, looks set to come in third behind the Fatah (Conquest) alliance, led by former transport minister Hadi al-Amiri, who presides over the political wings of several Shia-led paramilitary forces.
Sadr faces a hard act to herd together enough groups from across Iraq's fragmented political spectrum to form a government.
Whether he can convince Abadi - a key member of the establishment Dawa party that has dominated Iraq for years - to turn his back on his former stablemates and team up remains a major question.
Al-Sadr's list is leading the popular vote count, followed by a list linked to Iraq's predominantly Shiite paramilitary forces that fought alongside Iraq's army in the war against IS militants.
Sadr is one of the few Iraqi politicians who is opposed to both the presence of American troops in Iraq and the overbearing influence neighbouring Iran exercises over the country.
Sadr's bloc did not run in the remaining two provinces, Kurdish Dohuk and the ethnically mixed oil province of Kirkuk. Whoever wins the most seats must negotiate a coalition government in order to have a majority in parliament.