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As Iraq’s government presses the United States for a deadline to withdraw its troops, top U.S. military officials Monday cautioned against pushing Iraqi forces to take control too quickly — a warning underscored by bombs that killed at least 35 people.

The attacks, on the eve of Gen. David Petraeus’ hand-over of command of U.S. forces in Iraq to Lt. Gen. Raymond Odierno, were a reminder of the challenges ahead as Odierno tries to hold on to security gains with fewer U.S. troops.

Odierno will be elevated to full general before the hand-over, which comes 19 months after Petraeus arrived in Iraq and instituted counterinsurgency tactics credited with leading the turnaround in violence.

Odierno’s No. 2 commander, Lt. Gen. Lloyd Austin, warned Monday that just as security gains were lost in 2005 when Petraeus’ predecessor hurried Iraqi security forces to stand on their own, more recent gains also were fragile.

“I am not sure pushing them forward is the right thing to do,” Austin said of Iraqi security forces. “We tried that once before, and it didn’t work.”

At a meeting with journalists, Austin said Iraqi forces could be prepared to stand on their own by 2011, the date Iraq’s government would like as a deadline for a U.S. troop withdrawal, but that developments “could slow down their evolution.”

U.S. officials have noted that the Iraqi forces, while greatly improved, still suffer a lack of logistical, intelligence and other support expertise.

Earlier, Defense Secretary Robert Gates, who arrived in Iraq on Monday for the hand-over, said U.S. forces would remain “seriously engaged” here but that “the areas in which we remain seriously engaged will continue to narrow.”

In his farewell letter to the 146,000 U.S. troops in Iraq, Petraeus said their accomplishments in the past 19 months “have, in fact, been the stuff of history.” But he added that their tasks in Iraq “are far from complete, and hard work and tough fights lie ahead.”

Monday’s carnage, including the worst bombing in Baghdad in weeks, showed the unpredictable nature of Iraq’s security situation. Police said two car bombs timed to go off minutes apart along the same busy Baghdad street killed at least 13 people and injured 35.

Hours later, a woman walked into a party being thrown at a police officer’s home in Balad Ruz, 50 miles northeast of Baghdad, and blew herself up. Police said 22 people were killed.