Seen as a blow to US plans to bring stability to war-ravaged Iraq, the car bombing left up to 10 people dead, eight wounded and vehicles ablaze outside the high-security compound housing the occupation headquarters in Baghdad.
But the Bush administration vowed Monday's assassination would not delay handover plans scheduled for 30 June.
"On June 30, the flag of a free Iraq will be raised, and Iraq's new interim government will assume sovereign authority," US President George Bush said in a statement reacting to the car bombing.
Salim was the leader of the Iraqi Governing Council (IGC) for May. The leadership is rotated on a monthly basis.
Claims of responsibility
Claims of responsibility for the attack were made in a statement posted on an Iraqi website:
"This morning, two heroic members of the Arab Resistance Movement/Rashid Brigades - Ali Khalid al-Jabburi and Muhammad Hasan al-Samarrai - carried out a qualitative heroic operation that led to the killing of the traitor and mercenary Izz al-Din Salim," said the statement posted on www.anbaar.net.
"The brigades pledge to the people of our nation that they will (continue to) struggle until the liberation of glorious Iraq and precious Palestine," added the statement, the authenticity of which could not be verified.
A Kurdish member of the council, Mahmud Uthman, said the attacker had probably been waiting for Salim.
The brief statement claiming responsibility, however, did not refer to the alleged attackers as "martyrs", the term usually used in connection with "martyrdom operations".
The car bombing occurred near
US headquarters in Baghdad
The website, adorned with an old Iraqi flag at the top with another, cut Iraqi flag superimposed on it, opens with the words: "Al-Anbar site, voice of all Iraqis, direct from Baghdad."
"Come into Al-Anbar forum; hold your head high, you are in Falluja," it says.
Falluja, in the province of Al-Anbar west of Baghdad, is a hotbed of resistance to US-led forces occupying Iraq and was the site of fierce fighting last April.
"We are a nation to whom God gave glory in Islam. If we seek glory elsewhere, God will humiliate us," the site adds.
US investigating claim
Brigadier General Mark Kimmitt, deputy director of military operations for the US-led occupying forces in Iraq, said they were examining the website claim, but first suspicions pointed to Jordanian Abu Musab al-Zarqawi.
"We don't know if that's a cover for the Zarqawi network or it's an actual organisation," Kimmitt told a news conference.
"All of those indicators, suicidal, spectacular, symbolic, line up here but we have this new group that has come in and we don't know who this group is. We're going to have to do some analysis on it," he said.
Al-Zarqawi has been linked to Usama bin Ladin's al-Qaida movement and has a $10-million price on his head by the US government.
The US Central Intelligence Agency said on Thursday there was a "high probability" al-Zarqawi was shown in a video last week decapitating US hostage Nicholas Berg, who vanished in Iraq in April.