White House press secretary Dana Perino said Bush spoke to al-Maliki about the Quran shooting incident during a regularly scheduled videoconference on Monday. She said Bush expressed his "serious concern."
"He told the prime minister that we take this matter seriously, and he noted that the soldier had been reprimanded and removed from Iraq by his commanders," Perino said.
A statement issued by al-Maliki's office said Al-Maliki told Bush of the "disappointment and anger of the people and government of Iraq over the soldier's disgraceful action," the statement said.
Bush told al-Maliki that the sniper would face trial, it added.
Separately, the statement said an Iraqi Cabinet meeting Tuesday called for the "severest" punishment against the sniper and warned of "grave consequences" if similarly offensive actions were committed in the future.
It also called on commanders of U.S.-led foreign troops in Iraq to educate their soldiers on the need to respect the religious beliefs of Iraqis.
The U.S. military said Sunday it had disciplined the sniper and removed him from Iraq after he was found to have used Islam's holy book for target practice on May 9. The copy of the Quran was found two days later by Iraqis on a firing range in Radwaniyah, west of Baghdad, with 14 bullet holes in it and graffiti written on its pages.
On Saturday, the top American commander in Baghdad, Maj. Gen. Jeffery Hammond, and other officers held a formal ceremony apologizing to tribal chiefs in Radwaniyah.
Bush's apology followed similar moves by the No. 2 U.S. commander in Iraq to placate the Iraqis, apologizing in separate meetings Monday with al-Maliki, Vice President Tariq al-Hashemi and parliament speaker Mahmoud al-Mashhadani.
The U.S. military said Lt. Gen. Lloyd J. Austin III paid individual visits to al-Maliki, a Shiite Muslim, al-Hashemi and al-Mashhadani, both Sunni Arabs - moves underlining the American eagerness to make amends for the incident, particularly among Sunni Arabs who have become key allies in the fight against insurgents.
In their meeting in his office, al-Hashemi, the top Sunni Arab in the government, told Austin that "the feelings of bitterness and anger cannot be eased unless there is a deterrent punishment and real guarantees" such an incident won't be repeated, according to al-Hashemi's office.
Al-Hashemi expressed his appreciation for the visit but asked for a written apology from the U.S. military.
Austin underlined in all three meetings that "the soldier had in fact been removed from Iraq. He assured them that the matter was serious and that we hold our soldiers accountable for their actions," a U.S. military statement said.
Al-Hashemi's Iraqi Islamic Party also issued a tough statement Monday saying that an apology alone was not enough and the U.S. military should impose the "severest punishment" on the soldier to ensure others do not repeat his act.