Baghdad, Iraq ? America’s two top officials in Iraq on Thursday sought to calm Iraqi anger about allegations that U.S. soldiers were involved in the rape-murder of a girl, promising an open investigation and calling such acts “absolutely inexcusable and unacceptable.”

The rare joint statement from U.S. Ambassador Zalmay Khalilzad and Gen. George Casey, the senior U.S. commander in Iraq, came as military officers investigated the apparent failures of leadership to keep a close watch on American troops.

Several groups of soldiers and Marines are under investigation for alleged slayings of unarmed civilians, and three U.S. soldiers were killed by insurgents last month after they apparently were left alone despite procedures designed to prevent that.

The joint statement underscored U.S. efforts to contain the political damage that the March 12 death of a girl and three relatives has caused among an Iraqi public increasingly weary of foreign troops.

“The alleged events of that day are absolutely inexcusable and unacceptable behavior,” the statement said. “We will fully pursue all the facts in a vigorous and open process as we investigate this situation.”

Khalilzad and Casey promised a vigorous investigation and prosecution of the case and pledged to “work closely with the government of Iraq to ensure transparency as we complete the investigatory and legal processes.”

Ahmed, 9, left, and Mohammed Qassim Hamza, 11, brothers of the young Iraqi girl who was allegedly raped then killed along with family members, sit at the stream behind their home in Mahmoudiya, south of Baghdad, Iraq. Former U.S. Army Pvt. Steven D. Green pleaded not guilty to rape and four counts of murder Thursday in Kentucky. At least three other U.S. soldiers still in Iraq are under investigation in the attack.

Iraqi Prime Minister Nouri al-Maliki has called for an independent investigation into the attack and a review of the agreement granting U.S. forces immunity from prosecution by Iraqi courts.

Ex-soldier Steven D. Green has been charged with rape and four counts of murder in the March 12 incident in Mahmoudiya, 20 miles south of Baghdad. At least three soldiers still in Iraq are under investigation, including a sergeant, a specialist and a private first class, a defense official in Baghdad said Thursday.

The case has raised questions about adherence to procedures set for U.S. troops in Iraq, as well as discipline within the suspects’ unit. The soldiers were from the 1st Battalion, 502nd Infantry Regiment, 101st Airborne Division, the same unit hit by the insurgent killings of three soldiers last month.

Spokesmen for the 101st Airborne and the Multinational Corps of Iraq refused to discuss the case on the record because of its sensitivity.

The U.S. military has strict rules for soldiers operating outside their bases, designed to ensure they are under supervision and to protect them. All soldiers leaving their bases are supposed to be accompanied by a noncommissioned officer and travel in at least two vehicles.

The rape-murder investigation has raised questions whether there are problems with how the military operates because soldiers allegedly left their post without someone raising questions.

According to a federal affidavit, Green and at least two other soldiers drank alcohol, abandoned the checkpoint they were manning, changed clothes to avoid detection and then headed to the victims’ house about 200 yards from a U.S. military camp. A fourth soldier stayed in uniform, the affidavit said.

Nearly all those steps are violations of regulations, U.S. officials say.