The Army planned to announce the decision Tuesday afternoon, the officials said, speaking on condition of anonymity.
Meanwhile, militiamen launched a barrage of mortar shells against a U.S. base in the holy city of Najaf and government buildings guarded by Bulgarian forces in Karbala on Tuesday, a day after intense clashes in Najaf that killed up to 20 Iraqis.
No coalition troops were killed in the violence, but four U.S. soldiers of the 1st Infantry Division died after their vehicle overturned during a combat patrol north of Baghdad, according to the Army.
U.S. artillery, meanwhile, shelled rebel positions late Monday after insurgents fired on aircraft near Baghdad airport. Four Iraqi insurgents were killed, the military said Tuesday.
In other developments:
Pentagon officials had said in recent weeks that they were prepared to replace a portion or all of the 20,000 1st Armored and 2nd Cavalry soldiers who are on extended duty in Iraq if Gen. John Abizaid, the top commander of U.S. forces in the Middle East, believed they were needed.
Abizaid and his subordinate commanders have used the 2nd Armored Cavalry and 1st Armored to deal with outbreaks of violence in and around the Shiite holy city of Najaf and elsewhere in central Iraq.
At the moment there are about 138,000 U.S. forces in Iraq. That number was to have fallen to about 115,000 this spring, but a surge in anti-occupation violence caused Abizaid to bolster the force.
The Army and Marine Corps are hard-pressed to find substantial additional troops for Iraq duty. Of the Army's 10 divisions, parts or all of nine are already deployed in Iraq or Afghanistan.
Under the order to be announced Tuesday, about 5,000 Marines and a contingent of about 5,000 soldiers from the 10th Mountain Division, based at Fort Drum, N.Y., will go this summer to relieve the 1st Armored Division and the 2nd Armored Cavalry Regiment, whose soldiers were due to come home in April but were extended by three months.
The 10th Mountain Division, which is mainly a light infantry unit, has soldiers in both Iraq and Afghanistan. The group that will go to Iraq this summer is a task force built mainly around the 2nd Brigade, known as the "Commandos," another official said.
Details about the 37,000 National Guard and Reserve troops who are being alerted for Iraq duty were not immediately available. They will provide support for the three National Guard combat brigades that were notified earlier this year that they will be going to Iraq for one-year tours late this year or early in 2005. A large proportion of the 37,000 are Army Reserve, one official said.
Sporadic overnight mortar attacks on the U.S. base in Najaf followed intense fighting on Monday between U.S. forces and militiamen loyal to radical anti-American cleric Muqtada al-Sadr.
The U.S. military moved soldiers to the base inside the city last month after Spanish peacekeepers withdrew from the country.
But the military has been cautious about returning fire. Al-Sadr's office is located only a few yards from one of the holiest Shiite shrines and not far from the U.S. base. U.S. officials repeatedly have accused militiamen of storing weapons in shrines and mosques.
Al-Sadr's forces, which launched an uprising across southern Iraq in early April, have stepped up attacks in recent days — apparently either to pressure U.S. officials to negotiate an end to the standoff or to goad troops into retaliating and raising Shiite anger.
On a second front, a senior Marine officer said Tuesday that the new Iraqi military force that is replacing U.S. troops in Fallujah, 35 miles west of Baghdad, is "meeting expectations" in bringing calm to the city.
An all-Iraqi force of up to 1,100 began moving into positions from withdrawing Marines last week as part of an agreement to restore order in the city, the site of a nearly monthlong siege that left 10 Marines and several hundred Iraqis dead.
Maj. Gen. Mohammed Abdul-Latif, who opposed Saddam Hussein, was preparing to take over as head of the new force, subject to a final background check by U.S. officials. Abdul-Latif would replace another general who may have been involved in Saddam-era repression.
Fallujah residents have been celebrating what many see as a victory over the U.S. Marines. Masked and armed insurgents have moved freely in the city's streets, sometimes standing alongside Iraqi policemen.
U.S. officials say the Fallujah Brigade will crack down on hard-core guerrillas in the city even though the force itself will likely include some gunmen who had been involved in fighting against the Marines.