Baghdad, Iraq (CNN) -- Iraq's two top vote-getters tried again this week to break an impasse in forming a new government, more than four months after national elections produced no clear winner.
Prime Minister Nuri al-Maliki met Tuesday evening for a third time since the vote with Ayad Allawi, a former interim prime minister and the head of the Iraqiya bloc.
Allawi's mostly secular coalition won two more seats than al-Maliki's Shiite State of Law coalition but neither won the majority needed to form a new government.
Since the election, al-Maliki's coalition merged with the other main Shiite bloc, the Iraqi National Alliance. But the mega-Shiite coalition still fell four seats short of a mandate.
However, the alliance has been unable to nominate a prime minister. Supporters of radical Shiite cleric Muqtada al-Sadr, who hold 39 seats, have refused to accept al-Maliki for a second term.
Al-Maliki and Allawi agreed Tuesday to intensify dialogue between the political blocs but both men say they should get the first chance to form a new government and both want to become prime minister.
No deals were reached and the stalemate continues at a critical period for Iraq. The United States is drawing down troop levels to a non-combat force of 50,000 by September 1. Soldiers of the 82nd Airborne Division were packing up this week to return home.
And Iraqis, though accustomed to the slow pace of their politicians, are weary of a way of life governed by a lack of basic services and most importantly, a lack of security.
In the past few days, at least 50 people have been killed and dozens others wounded in a number of attacks across the country. On Wednesday morning, three roadside bombs exploded in Baghdad, killing one civilian and wounding seven others.
The key meeting between the two Iraqi leaders came on the heels of Allawi's talks Monday with al-Sadr. Allawi's office described the discussion as going "very well."
"The reception was very cordial and both leaders shared many identical views, including respecting the democratic process to take its course for the benefit of Iraq," said a statement from Allawi's office. "Moreover, they were very supportive to have an inclusive, national and accountable government capable to deliver a responsible program to serve Iraq and treat all Iraqis equally."
It was the first meeting between Allawi and al-Sadr, and both agreed to keep in close contact, the statement said.
Iraq's new parliament, the second elected to a full term since the overthrow of Saddam Hussein in 2003, has met only once since the March 7 elections. The 325 new lawmakers took their oath of office during a largely symbolic 15-minute session on June 14, then suspended the session for politicians to continue trying to hammer out agreements.