“I think we may reach an agreement with seven armed groups that visited me and I met with them,” his office said in a statement on Sunday without indicating when the meeting took place.
Talabani's spokesman Kamran Qaradaghi declined to identify the seven groups, although they were presumed to be Sunni Arab insurgents.
It was the first time a senior Iraqi official has acknowledged meeting figures from the insurgency, although US officials have said privately that they have conferred directly with Iraqis who claimed to have contacts with insurgents.
However, Ibrahim al-Shammari, spokesman of the Islamic Army in Iraq, denied that his group had met Talabani or any US officials.
“Our strategic choice is to resist the occupation by armed force,” al-Shammari told Al Jazeera television. “We neither met the Americans, nor the US ambassador, nor with the (Iraqi) government because it is an illegal government with no credibility.”
Last year, Talabani, a Kurd, had offered to meet the representatives of insurgent groups except al-Qaida in Iraq or Saddam Hussein loyalists.
The statement said Talabani had made the comments on Saturday during a cultural festival in Kurdistan, the Kurdish-self ruled area in the north.
Talabani said American officials had met with “some armed groups,” but Qaradaghi said there were no Americans present during the meeting with the seven groups.
The statement also quoted Talabani as saying that al-Qaida in Iraq, led by Abu Musab al-Zarqawi, had declared a “genocide against the Iraqi population.”
“But there are groups other than the Saddamists and Zarqawists who joined the armed operations for the purpose of fighting the occupation,” Talabani was quoted as saying. “We are trying to have a dialogue with them to join the political process.”