Iraq's President Jalal Talabani has said he is willing to speak to insurgents if they want to talk to him.
Mr Talabani said he was president of all Iraqis - and would listen
Addressing a national reconciliation conference in Cairo, he said he was "responsible for all Iraqis" and wanted to "listen... even to criminals".
But he said Saddam Hussein supporters and religious extremists had no role in the country's political process.
There have been reports of contacts between insurgents and the Iraqi government, which have been denied.
Donald Rumsfeld, the US defence secretary, said in June the US government regularly facilitated contacts between the Iraqi government and insurgents.
Mr Talabani immediately denied it.
"The Iraqi government has nothing to do with the negotiations with insurgents," he said at the time.
It was not immediately clear exactly what he was offering at the Arab League-sponsored conference on Sunday.
"If those who describe themselves as the Iraqi resistance want to contact me, they are welcome," he said.
"I am committed to listen to them, even those who are criminals and on trial."
"But of course that does not mean I will accept what they say," the president told a news conference.
Government leaders have previously said they would talk to opposition forces who were willing to lay down their arms - but not those who are responsible for killing Iraqis.
There have been unconfirmed reports that Mr Talabani has met with representatives of the opposition during the conference in Cairo.
There is pressure from within Iraq and from the west to try to strike a deal that would ease, if not end, the violence in Iraq, the BBC's Ian Pannell in Cairo says.
Wave of violence
Iraq was struck by a particularly bloody wave of bombings as the conference took place in Cairo.
More than 50 people were killed and many others injured on Saturday.
In one incident, at least 35 people died and 40 were wounded in a suicide car bomb attack on a Shia funeral procession near Baquba.
A car bomb attack on a crowded south Baghdad market left 13 dead and injured at least 20. Another attack in the city centre wounded at least four people.
And roadside bombs targeting US patrols killed five soldiers and wounded five others near Baiji, in north Iraq.