Al-Jibouri said the Accordance Front's decision was taken after al-Maliki objected to a candidate for a cabinet position.
He said the party drew up a list of candidates for six cabinet posts to hand to the government for approval, but al-Maliki rejected the nomination for the planning ministry.
Al-Maliki refused to give the Sunni bloc an extra government post as a compromise, al-Jibouri said.
Officials from al-Maliki's office were not immediately available for comment.
A statement on Tuesday from the office of Tareq al-Hashemi, a senior member of the Accordance Front who is also a vice-president of Iraq, said he believed the talks would succeed despite disagreements.
"We achieved significant progress on returning to the government although there are some differences in points of view over some ministries and candidates," he said.
"And we hope that in the coming days that this will be resolved and the Accordance Front will return to the national unity government."
Sunni Arabs have little voice in a cabinet dominated by Shia Arabs and Kurds.
Since becoming prime minister in May 2006, al-Maliki has faced constant criticism from the community that he has promoted the interests of the majority Shia ahead of the country's other sectarian and ethnic groups.
But he won praise from Sunni Arab politicians after launching a crackdown on Shia militias in Baghdad and the southern oil city of Basra.
The government has also begun releasing Sunni Arab prisoners under a new amnesty law.
Sunni Arabs were dominant under Saddam Hussein and anti-government fighters have drawn support from the community.
Persuading the bloc to rejoin has been a main aim of the US policy in Iraq, and is widely seen as a vital step in reconciling the country's factions after years of conflict.