0236 GMT February 25, 2020
The alliance includes Shia cleric Moqtada al-Sadr's Sairoon coalition, outgoing Prime Minister Haider al-Abadi’s Victory bloc, Shia cleric Ammar al-Hakim’s National Wisdom Movement and former premier Iyad Allawi’s National coalition.
After the meeting, the four blocks announced late on Sunday a preliminary agreement to form a coalition.
"We agreed today to form a core for an alliance, seeking to form a parliamentary bloc that can form the government. We have decided at this meeting to open up to our other partners to contribute together in the formation of this (largest) alliance," said the blocs in a statement on Sunday.
The announcement also confirmed the blocs' commitment to taking an anti-sectarian approach to the process of forming a new government.
"The coalition is determined to work hard to build a state of citizenship, justice, equality and the provision of a decent life for all our people," the statement said.
Confirming the progress of the talks, Kadhim al-Shimmary, a leading figure in the National bloc said: "We had a successful meeting and agreed to form a coalition among us.
"We are now waiting to see if we will be able to form the largest bloc," he added.
The announcement came as Iraq's Supreme Court ratified the final results of the May 12 parliamentary elections, setting in motion a 90-day constitutional deadline for the top parties to form a coalition government.
Many Iraqis disputed the results of the vote, alleging widespread electoral misconduct but a nationwide recount of votes on August 10 did not change the number of seats Sadr's bloc won.
According to the commission, only one seat from Iraq's Baghdad coalition had moved to the second-placed Al-Fatih bloc, giving it 48 instead of 47 assembly seats.
But while Sadr retained his lead, his potential alliance with Abadi's bloc and the others does not grant him the 50 percent plus one – or at least 165 seats – needed to form a majority bloc.
The Sairoon alliance won the largest number of parliamentary seats at 54, while the Victory alliance, which came in third place, won 42 seats.
Together with the Wisdom bloc, which won only 19 seats, and Allawi's National bloc, which won 21 seats, the potential alliance has 137 seats - 28 seats short of a majority bloc.
In a televised speech earlier on Sunday, al-Abadi called on the political blocs to accelerate their negotiations, and on Iraqi President Fuad Masoum to invite the new parliament to hold its first session soon.
Following the Supreme Court's ratification of final results, incoming MPs are now expected to hold a first session to elect a new assembly speaker.
Within 30 days of that first session, a two-thirds majority of the assembly will elect the country's next president, who will then task the largest bloc in parliament with drawing up a government.
The new government will have to be referred back to parliament for approval.
Al Jazeera and Anadolu contributed to this story.