However, Allawi's party left the door open for a return to talks.
"We have asked him to apologise. Without an apology, we are not going to negotiate with him anymore," she said.
While Allawi is a Shia, like al-Maliki and the majority of Iraqis, his bloc claimed most of its support from the predominantly Sunni regions of western and northern Iraq in a March 7 general election.
Allawi's Iraqiya achieved a narrow victory in the general elections, when it came first with 91 seats out of Iraq's parliament 325 seats. Al-Maliki's State of Law came second with 89 seats.
More than five months after the vote, neither blocs have yet managed to form a governing coalition with the necessary majority.
The resultant political uncertainty has raised security concerns with analysts saying that armed groups might exploit the situation to their advantage.
They fear a spike in violence from the anti-government fighters for destabilising the country and undermining state authority.