The new leader of al-Qaeda in Iraq will be "brought to justice", US President George W Bush has pledged.
Mr Bush's aides have said the two-day talks are crucial for Iraq
Abu Hamza al-Muhajir was named as the successor to Abu Musab al-Zarqawi, killed in a US air strike last week.
Speaking during two days of talks with key advisers over future US strategy in Iraq, Mr Bush was quick to insist that Muhajir would be "on our list".
A website confirming Muhajir's role described him as "knowledgeable", with a history of fighting a holy war.
Mr Bush described Zarqawi's death as a "major blow" to al-Qaeda's operations in Iraq, but admitted it would not end the insurgency.
"The successor to Zarqawi is going to be on our list to bring to justice," he added.
Two car bombs exploded within 30 minutes in the northern city of Kirkuk on Tuesday, killing at least 15 people and wounding 15, police said.
Mr Bush was speaking at Camp David, the Maryland retreat where he is hosting two days of talks with his cabinet and senior military figures designed to outline a way forward for the US in Iraq.
He gave few details after the first day of talks, but rebuffed suggestions that the US was preparing to pull troops out of Iraq.
"Whatever we do will be based upon the conditions on the ground," he said, adding that the US was still "understanding" Iraqi capabilities.
He did suggest that Iraq should garner greater benefits from its vast oil reserves, boosting production and ring-fencing revenues for national reconstruction.
Members of Prime Minister Nouri Maliki's new Iraqi cabinet will participate in the talks on Tuesday, joining the meeting via video link.
The BBC's James Coomarasamy in Washington says the White House hopes this conference will bolster the Iraqi cabinet and increase US public confidence in Mr Bush's handling of the situation there.
The statement from al-Qaeda in Iraq said its council had "unanimously agreed" on Zarqawi's successor.
"We ask God that he... continue what Sheikh Abu Musab began," it added.
Abu Musab al-Zarqawi brought al-Qaeda in Iraq world notoriety
Muhajir was not among the names al-Qaeda analysts had expected as a probable successor, and is believed to be a pseudonym.
Analysts say the name al-Muhajir - which is Arabic for immigrant - suggests he is not Iraqi.
The group has been quick to declare their operations will continue despite the loss of their exceptionally violent leader, the BBC's security correspondent Frank Gardner says.
Our correspondent says military analysts will be watching to see if al-Qaeda in Iraq continues its campaign against Shia Muslims - or focuses its attacks more narrowly to broaden support among Iraqis.
Zarqawi's successor was named as the US military announced that post-mortem analysis revealed Zarqawi did die from injuries consistent with a bomb blast.
He died after US planes dropped two 500lb (230kg) bombs on a safe house near the city of Baquba on Wednesday.
US military doctor Steve Jones told reporters the cause of death was a blast injury to the lungs, and said tests showed no evidence of beatings or gunshots.
Major General William Caldwell said Zarqawi had taken nearly an hour to die after the strike.