He urged Sunni groups to participate in the two day reconciliation meeting.
"If you want to fix something, you can't do it by boycotts. Everybody should participate," he said.
But the National Concord Front said only certain members of its organisation had been invited to attend the meeting.
A spokesperson for the Accordance Front said it would not attend; not because it was against reconciliation, but because invitations had been sent to specific members and not the coalition collectively
Al-Maliki also said the bloc was protesting at the way Iraq handled the case of a former deputy minister who was acquitted on allegations of organising Shia death squads that targeted Sunnis.
Earlier the month, an Iraqi court freed Hakim al-Zamili, a former deputy health minister, saying there was no evidence against him.
Brigadier General Hamid al-Shammari, the health ministry’s security chief, was also acquitted in the same trial.
"The Zamili case has emerged as a big obstacle in reconciliation, because the way it was handled has not satisfied the Concord Front," Abdallah said.
The two-day conference in Baghdad comes as a US military commander said that progress towards lasting peace in Iraq has been too slow.
General David Petraeus told the Washington Post that "no one" in the US and Iraqi governments "feels that there has been sufficient progress by any means in the area of national reconciliation".
In recent months, the US has sent 30,000 extra troops to Iraq in what it calls an attempt to rein in sectarian violence.
During an unscheduled visit to Iraq on Monday, Dick Cheney, the US vice-president, said that he was wary of large-scale US troop cuts.
He said that any advances in security for Iraqis would be wiped out should troops be pulled out of the country.
The purported aim of the troop 'surge' is to give Iraqi leaders a chance to pass a raft of laws intended to attract armed groups back into mainstream politics, but parts of the legislation package have stalled in parliament.
The peace talks are the second attempt by al-Maliki to end sectarian fighting that has gripped the country since suspected Sunni fighters blew up a Shia shrine in February 2006.