Talabani, a Kurd, announced on Monday he would convene parliament on Sunday, just meeting a constitutional deadline for him to summon lawmakers after the final results of the 15 December parliamentary election being certified.
But nearly three months after the election, Iraq's political leaders are still fighting over who should be the new prime minister in Iraq's first full-term four year government.
The Shia Alliance, by far the biggest bloc in the new parliament, is facing mounting pressure from would-be partners to get rid of Ibrahim al-Jaafari, the prime minister, who critics say has failed to stop sectarian violence that has killed hundreds and pushed Iraq to the brink of civil war.
The political stalemate has complicated efforts to form a national unity government of Shias, Sunnis and Kurds that Washington is promoting as the best hope of stabilising Iraq and allowing it to begin pulling out its troops.
Rida Jawad al-Takki, a senior member of SCIRI, the biggest Shia political party and a mainstay of the Alliance coalition, said: "We have decided to ask Talabani to postpone parliament's first session for a few days. We are discussing the demands from the other groups to change our nomination."
Another SCIRI official, who declined to be named, said Husain al-Shahristani - a Shia deputy speaker in the outgoing parliament - had met Talabani to ask for the postponement.
"We need more time in the Alliance. We want the meeting of parliament to be postponed by between two and nine days," the second SCIRI official said.
"It will probably be postponed about a week."
There was no immediate comment from Talabani's office.