Officials in both political groups said on Thursday that the deal requires the government to begin discussion on the return of about 100,000 Kurds to the oil-rich northern city of Kirkuk.
"As for Kirkuk, we agreed to solve the issue in two steps. In the first step, the new government is committed to normalising the situation in Kirkuk," said Fuad Masum, a member of the Kurdish coalition, who served as head of Iraq's former National Council.
"The other step regarding annexing Kirkuk to Kurdistan is to be left until the writing of the constitution."
Masum added that "the upcoming government is obligated to normalisation in Kirkuk, the return of deported Kurds to their main areas".
A member of the alliance who has participated in negotiations with the Kurds also said the new government would deal with the issues of Kirkuk and Kurds that were deported during the time of Saddam Hussein.
"We agreed with the Kurds that these two issues are to be solved through the government and they agreed on this and they demanded that things be settled as soon as possible.
"We told them that the issues will be discussed as soon as the central government is formed," said Ali al-Dabagh, a member of the Shia Political Council.