The group confirmed tonight its choice of al-Maliki. The alliance says it will present his name and of other candidates to a session of parliament tomorrow in order to form a new government.
Iraqi's largest Sunni Arab coalition says it welcomes the choice.
Al-Maliki is an ally of Prime Minister Ibrahim al-Ja'fari, whose nomination had sparked opposition from Sunni Arab and Kurdish leaders. Al-Ja'fari withdrew under pressure yesterday.
Sa'di Ahmad Pirah, a leading member of the Patriotic Union of Kurdistan spoke today to Radio Free Iraq about the political situation.
"The announcement of Dr. [Ibrahim] al-Ja'fari that he would withdraw from his nomination for the position of prime minister is a positive step," Pirah said. "By this step he has helped Iraq and the democratic process in Iraq."
With the deal on al-Maliki, Shiite, Sunni, and Kurdish parties also have said to agree on nominees to fill the other top posts.
Under the proposed deal, Jalal Talabani, a Kurd, would remain as president for a second term. Sunni Arab Tariq al-Hashimi and Shi'ite Adil Abd al-Mahdi would hold the two vice-president spots. Mahmud al-Mashhadani, a Sunni, would become parliament speaker with two deputies: Khalid Attiya, a Shi'ite, and Arif Tayfour, a Kurd.
(with additional agency material)