But the new president acknowledged that the United States – whose military forces have been a prime target of attacks – was opposed to using militia forces.
"In my opinion, Iraqi forces, popular forces and government forces, are now ready to end this insurgency," Talabani said.
He, however, said "there is a kind of thinking inside the government that they must not use the popular forces, for example from Peshmergas, from al-Badr, from armed forces of opposition parties".
But he nevertheless argued that "we have inner forces to eradicate terrorists", and that they should be brought into the fight.
Al-Badr is the successor of the Badr Brigades, the armed wing of Iraq's main Shia political party, the Supreme Council for the Islamic Revolution in Iraq (SCIRI), whose leaders lived in exile in Iran and were funded by the Islamic republic until Saddam Hussein's downfall in 2003.
"In my opinion, Iraqi forces, popular forces and government forces, are now ready to end this insurgency"
Iraqi interim president
In an interview with BBC, Talabani said it would take "years" to bring armed groups to heel if the government waited for official security forces to be organised.
On Iraq's new constitution, Talabani reiterated his refusal of an Islamic government, saying it would be "impossible" given the country's "mosaic society" made up of Shia, Sunnis, Arabs, Kurds and Christians.
Even "Islamic parties are not asking for an Islamic government", he said.
On the fate of Saddam Hussein, who is awaiting trial, Talabani said he would not sign a death warrant in the event that he was convicted and sentenced to execution.
"Personally, no, I won't sign," he said. "But you know, the presidency of Iraq are three people. These three must decide. So I can be absent. I can go on holiday and let the two other vice-presidents decide."
Meanwhile, the largest political bloc in Iraq's new government has demanded the ousted president's execution if he is convicted of war crimes.
"This is something that cannot be discussed at all," Ali al-Dabagh, a spokesman for the United Iraqi Alliance, which holds 140 seats in Iraq's 275-member National Assembly, said on Monday.
"We feel he is a criminal. He is the number one criminal in the world. He is a murderer," the spokesman said, adding Talabani should step down if he was not willing to sign the death warrant.