Talabani told reporters in a press conference with Barzani, Kurdistan's president, at the northern resort town of Dukan: "I am going back to Baghdad tomorrow and I will demand in the name of the people of Kurdistan and Masoud Barzani that article 58 be applied immediately."
"The United Iraqi Alliance and the Kurdistan alliance agreed on this before the government was formed."
Shias swept the January parliamentary election but were unable to form a government without entering into an alliance with the Kurds.
More than two months of intense negotiations between the two sides culminated in a memorandum of understanding that said the issue of Kirkuk would be handled in accordance with article 58 of the Transitional Administrative Law (TAL), the interim laws passed under the previous US-led occupation authority.
Return of deportees
Both sides agreed that the principals of the TAL would form the nucleus of the new constitution, which must be drafted by 15 August and put to a national referendum by 15 October, according to the political timetable.
Talabani said that, in accordance with article 58, Kurdish families deported from Kirkuk during ousted leader Saddam Hussein's government must be allowed back now and Sunni Arabs taken back to their original homes in central and southern Iraq.
"Jaafari's government must implement this immediately," repeated Talabani.
"The United Iraqi Alliance and the Kurdistan alliance agreed on this before the government was formed"
He, along with Barzani, fought Saddam's government for decades to secure Kurdish rights and managed to carve out the autonomous Kurdistan region in the early 1990s.
Talabani, who became Iraq's first Kurdish president in April, said the government must financially assist resettling Kurds and Arabs.
Barzani, who recently became president of Kurdistan, said he totally agreed with Talabani.
He has long pressed for a Kurdish federation with Kirkuk as its capital.
The Kurdish leaders did not say what they would do if their demands were not fulfilled, but the announcement is likely to anger Sunni Arabs and Turkmen who have long spoken about a Kurdish conspiracy to drive them out of Kirkuk.
It could also cause tensions with the Shia community. Prime Minister Ibrahim al-Jaafari, a Shia, said in an interview last week that the issue of the northern oil hub of Kirkuk was complicated and could take some time to resolve.