Maliki and Allawi were the top contenders for prime minister in last year's parliamentary elections. Allawi narrowly won the vote but was unable to form a unity government that would have given him Maliki's job.
Batoul Farooq, a lawmaker in the Shiite Iraqi National Alliance, said differences between the two leaders "may continue at the current time, but they will disappear," the Voices of Iraq news agency reports.
The rival leaders have been at odds since agreements were reached to form a unity government earlier this year. Maliki hasn't been able to fill some of his Cabinet positions with new leaders, and Allawi's party, Iraqiya, claims some of them are rightly theirs.
Maliki in late April threatened to dissolve the government within 100 days if differences continued.
Allawi complained that Maliki was monopolizing power, however.
"The political process is not owned by Maliki," he was quoted by Iraqi satellite channel al-Sumaria as saying. "It belongs to the Iraqi people."
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