Previous talks of a State of Law-INA alliance failed because Moqtada al-Sadr, a prominent Shia leader, refused any deal that would secure a second term for Maliki. Sadr's movement controls 39 of INA's 70 seats.
The INA is dominated by the Sadrist movement, a staunchly nationalist party, and the the Islamic Supreme Council of Iraq, a Shia party with close ties to Iran.
Officials from both blocs met yesterday at the home of Ibrahim al-Jaafari, the former prime minister who came out top in the Sadrist movement's informal referendumto choose the next prime minister.
Iraqi newspapers have speculated about several other possible candidates for the post, including Jafar al-Sadr, a cousin of Moqtada al-Sadr.
"The alliance brings them a step closer to forming a government, but there are still many unresolved issues, and some observers are saying these groups jumped the gun," said Al Jazeera's Mike Hanna, reporting from Baghdad.
The Sadrist movement was behind Maliki's nomination for the premiership in 2006, but Maliki angered the party by sending government troops, backed by US forces, to crush Sadr's Mehdi Army militia in 2008.
Maliki's State of Law Alliance won 89 seats in the March 7 election, and the INA won 70 seats.
That would give a merged bloc 159 seats, just shy of the required 163-seat majority to control the Iraqi parliament.
The Kurdish Alliance, comprised of the autonomous Kurdish region's two long-dominant political parties, holds 43 seats; it has previously promised to join a coalition with the main Shia blocs.
The Iraqiyya list, led by former premier Iyad Allawi, took the most seats in the election - 91 - but could be squeezed out of the government by a State of Law-INA merger.
Dhafir al-Ani, a senior member of the Iraqiyya bloc, told Al Jazeera: "It [the merger] is a blow to the will of the majority of Iraqi people, who voted for Iraqiyya. The new Shia merger, which is backed by Iran, would pull Iraq back to sectarianism."
Allawi has warned Maliki against excluding his party from government and last month suggested such a move could result in a return to the sectarian bloodshed that killed tens of thousands of people in 2006 and 2007.
Tuesday's announcement could escalate the debate over the Iraqi constitution's declarationthat "the biggest parliamentary bloc is entitled to form the government".
That provision was initially interpreted to mean that the coalition with the most seats after the election would have the first opportunity to form a government.
But Iraq's supreme court ruled on March 28 that the "biggest parliamentary bloc" could be one formed after the polls.
Iraqiyya insists that the court's decision is illegitimate and politically motivated.
State of Law and Iraqiyya could both see their representation change slightly in coming days: Iraq's Independent High Electoral Commission is recounting votes in Baghdad, which accounts for 70 seats in the 325-seat parliament.
But the recount is unlikely to mean significant changes; indeed, Maliki said last week that the recount will not change the balance of power in parliament.