Pro-Iranian militia chief Hadi al-Amiri's bloc won the second most votes in the parliamentary elections, making an alliance with him key to Sadr's effort to form a coalition with enough seats to hold a majority in parliament. As the top two seat-getters in the May 12 election, this would go a long way toward forming a government.
The two Shia figures said they would keep the door open for other winning blocs to join them in forming a new government.
The move by Sadr, who is staunchly opposed to Iranian involvement in the country, was unexpected by much of the political class as he had suggested unwillingness to work with Amiri and his bloc of pro-Iranian former fighters.
This is a surprising move as Sadr had campaigned heavily on the idea of Iraq being more independent, and less aligned with either the USA or Iran.
But at a joint press conference with Amiri in the Shiite holy city of Najaf, Sadr hailed the formation of "a true alliance to accelerate the formation of a national government away from any dogmatism".
"Our meeting was a very positive one".
He is said to be in talks with current Iraqi Prime Minister Haider al-Abadi's al-Nasr Coalition, the Hikma alliance, the National Alliance, and leading parties from the Kurdistan Region to form the next Iraqi government.
Confusion has gripped Iraq since Sadr's electoral alliance with communists won the vote.
The government report had recommended a recount of 5 per cent of votes but the outgoing parliament, in which over half of lawmakers including the speaker lost their seats, instead voted for a nationwide one.
Abadi called the fire a deliberate act and said the attorney general would bring charges against those who are trying to undermine the political process. It is not clear what positions within a coalition government are being offered to Amiri's bloc.
The Fatih alliance he led in the election was composed of political groups tied to Iran-backed militias who helped government forces dislodge Islamic State (IS) group militants from the third of Iraq they seized four years ago.