The incident is reported to have occurred on March 11 in Radhwaniya, near Baghdad, when the unnamed staff sergeant shot into a copy of the Quran and wrote an expletive inside it.
US military commanders in Iraq held a ceremony on Monday to formally apologise and presented a new copy of the Quran to tribal leaders in the area where the incident took place.
The news came as several Afghan lawmakers walked out of the parliament in Kabul on Tuesday, apparently in protest against the incident, witnesses said.
Lieutenant General Lloyd Austin, the top US commander in Baghdad, also told Iraq's prime minister and vice-president in separate meetings that the US viewed the matter seriously and that the soldier had been sent home.
But Tariq al-Hashemi, Iraq's vice-president and 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", according to a statement by al-Hashemi's office.
The incident was earlier strongly condemned by al-Hashemi and the Association of Muslim Scholars, which represents many of Iraq's mosques.
"This heinous crime shows the hatred that the leaders and the members of the occupying force have against the Quran and the [Muslim] people," the association said.
It added that it held both the US military and Iraqi government responsible for the incident.
Colonel Bill Buckner, a US military spokesman, said the military viewed the incident "as both serious and deeply troubling," but said it was an "isolated incident and a result of one soldier's actions".