Five months before the expiry of the US-led occupation force's United Nations mandate, Nuri al-Maliki said he was not calling for the early departure of the troops, who he said would remain for as long as Iraqi forces required assistance.
"Yes we will demand an independent Iraqi inquiry, or a joint investigation with Multinational Forces," al-Maliki told reporters during a visit to Kuwait, in his first public comments since the case came to light five days ago.
"We do not accept the violation of Iraqi people's honour as happened in this case. We believe that the immunity granted to international forces has emboldened them to commit such crimes and ... there must be a review of this immunity."
Politicians had demanded al-Maliki brief parliament on the case.
Under a 3-year-old mandate from the UN Security Council, the 140,000 or so US and foreign troops are immune from Iraqi law. Al-Maliki, in his third month in office, has urged US commanders to hold their soldiers to account under military law - something many Iraqis feel has not happened.
The rape and murder case is the fifth in a high-profile series of US inquiries into killings of Iraqi civilians in recent months, and comes at time when al-Maliki and Washington face delicate negotiations over a treaty to regulate the presence of the US-led force once the UN mandate expires in December.
The rape element in a conservative Muslim society - highlighted by al-Maliki's mention of "honour" - could make the case especially damaging for the US military, which has recently tightened procedures to crack down on rogue elements.
Major General William Caldwell, spokesman for the US military, said it "will leave no stone unturned" in getting to the bottom of the case. "There is not one service member who is immune."
Former private Steven Green, 21, is accused of shooting a couple and their young daughter near a checkpoint, then raping and killing the child's teenage sister. Three other US soldiers are suspected of taking part.
Also on Wednesday, in an off-the-cuff response to a journalist's question, al-Maliki said he hoped former president Saddam Hussein would be executed "soon, God willing."
His remark drew laughter from the assembled members of the press.
Asked who will ratify any death sentence against Saddam, Maliki said: "The leadership board will sign on his execution like it had signed on the execution of his predecessors."
The Iraqi president, Jalal Talabani, has said he rejects capital punishment in principle.
Saddam, who has stood trial on charges of killing Shia Muslims in the Iraqi village of Dujail in 1982, faces a new trial in August to answer charges of genocide in the killings of tens of thousands of Iraq's Kurds in 1988.