That would mean unifying Mr Barzani's and Mr Talabani's administrations, and holding region-wide elections.
He also spoke by telephone with President Talabani, Foreign Minister Zebari, and Council of Representatives Speaker Nujaifi.
Jalal Talabani, a Kurd, who was re-elected president by the parliament, asked Al-Maliki to form an administration.
Their task, says Barham Salih, the prime minister of Mr Talabani's regional government in Sulaymaniyah, is twofold.
Iraqi President Jalal Talabani has arrived in Germany for further treatment after a reported stroke, Berlin says.
"The Kurds will be a part of this Iraq, this united, democratic federation of Iraq, " Talabani said.
Talabani's office said the president is suffering from hardened arteries, but Othman said he had suffered a stroke.
CNN: 150 kidnapped from Iraqi finance ministry, minister says
Representatives from the parties met Sunday at Talabani's home to discuss the issue.
Still, Mr Talabani's Kurds may want Mr Allawi in to act as a counterweight to the UIA's pushier elements.
ECONOMIST: Iraq's Shias stick with the devil they know | The
President Jalal Talabani, a Kurd, and the US ambassador to Iraq, Christopher Hill, voiced support for the amended version.
Iraqi President Jalal Talabani will be meeting with his Iranian counterpart, Mahmoud Ahmadinejad, in Tehran to discuss bilateral relations.
Mr Talabani was reportedly rushed to the Baghdad Medical City on Monday evening.
German doctors earlier said Mr Talabani's condition had improved sufficiently to permit travel.
But Kurdish diplomat Qubad Talabani says Iraqi Kurdish leaders have learned not to get too close to their powerful neighbor.
German Foreign Minister Guido Westerwelle wished the 79-year-old Mr Talabani "a quick and full recovery", without providing any further details.
But the main issue is Talabani will always be more moderate than Barzani because Barzani shares the entire border with Turkey.
Ambassador QUBAD TALABANI (Kurdish Ambassador): Ultimately, we are neighbors, and I think this is something that I hope our American friends understand.
The bill, known as the Justice and Accountability law, must be signed by Iraqi President Jalal Talabani before it can take effect.
Iraq's political parties, meanwhile, reached agreement Sunday on the bylaws for the new government's Cabinet, according to a statement from Talabani's office.
The report by Iraqiya TV said the office of President Jalal Talabani announced Bashir's intention to attend the summit on March 29.
Diplomat Qubad Talabani says that's geopolitics as usual in the Middle East.
Almost certainly, Mr Talabani will be Iraq's president and Dr Ibrahim al-Jaafari, who heads the Dawa party within the Shia alliance, prime minister.
And one of the leaders of this front, Tariq al-Hashmi, said he sent a letter to Talabani outlining the reasons why he didn't come.
On Thursday, Vice President Joe Biden called Iraqi President Jalal Talabani to offer support for his efforts to foster dialogue, the White House said.
Aides said that included Iraqi Prime Minister Nuri al-Maliki and President Jalal Talabani as well as Iraq's vice presidents and other key political leaders.
Jalal Talabani, the Kurdish leader, has led a campaign to force the Alliance to rescind its decision to re-nominate Ibrahim al-Jaafari as prime minister.
Mr Talabani's illness comes at a time of heightened political tensions between Iraq's Arab-led central government and the semi-autonomous Kurdish region in the north.
Iraqi President Jalal Talabani must sign the law before it takes effect, and Petraeus and Crocker said its impact will depend on how it's implemented.
El anuncio lo hizo el nuevo presidente de Irak, Jalal Talabani.
Talabani added it had long been decided the whole country deserved a new one, and he said the national parliament would soon take up the issue.
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