BAGHDAD — A female suicide bomber struck a Shiite neighborhood Sunday morning in Baghdad, detonating her explosives after soldiers fired three rounds at her and she staggered to a nearby shop.

Two doctors and a police officer said four people were killed and 12 wounded. The U.S. military, however, said the only death was the bomber and two Iraqi army soldiers were wounded. The different tolls could not immediately be reconciled.

Two U.S. soldiers also were killed Sunday by small-arms fire in the volatile Diyala province, northeast of Baghdad, where troops are trying push out insurgents. The deaths announced by the U.S. military raised to at least 3,963 the number of service members who have died since the Iraq war started in March 2003, according to an Associated Press count.

The violence occurred on a day when a military spokesman said insurgent attacks across Iraq have dropped more than 60 percent since a U.S.-Iraqi campaign to cut down their influence began on Feb. 14.

In Baghdad, the female bomber appeared to be a beggar with something bulky around the midsection of her black garment, the military said in a statement. When troops directed her to raise her hands, she raised only one and had wires in the other hand.

"Sensing the potential danger, the soldiers fired three rounds," it said. "The woman staggered back to a nearby shop, where the blast detonated."

It wasn't clear whether the woman detonated the explosives herself, the military said.

Female suicide bombers have been involved in at least 18 attacks or attempted attacks since the war began, including the grisly bombings of two pet markets that killed nearly 100 people on Feb. 1. Iraqi and U.S. officials have said the women used in the pet market attacks were mentally disabled and apparently were unwitting bombers.

Separately, a car bombing Sunday in Mosul killed a police officer and two civilians, police there said. The U.S. military has said the northwestern city is the last major urban stronghold of al-Qaida in Iraq.

Iraqi authorities have been emphasizing security gains on the anniversary this week of the beginning of a joint crackdown to clear insurgent forces from Baghdad and surroundings with the help of some 30,000 additional U.S. troops.

Rear Adm. Gregory Smith, a U.S. spokesman in Baghdad, also quantified the successes at a news conference Sunday but warned more work remained to be done.

"A year ago, there were an average of 205 terrorist attacks each day across Iraq. Last month, we had tracked 82 — a decrease of over 60 percent," he said. Recently, there have been some days when the total number of attacks dropped below 40, the lowest level since 2004.

Smith, who praised a parallel buildup of Iraqi forces, cautioned that insurgents are still capable of spectacular attacks and said that Iranian funding of Shiite militia operations continues.

"Stability will take time and a continued commitment by all," he said.

The security crackdown has had particularly dramatic results in Baghdad, where the number of attacks peaked at 46 a day last June but dropped to 11 last month, Smith said.

U.S. Ambassador Ryan Crocker, meanwhile, said the Americans will not insist on long-term military bases in Iraq during upcoming negotiations between the two countries on a security agreement to replace the U.N. mandate for foreign troops that expires at the end of this year.

"I can say directly there is no American demand to set up American long-term bases in Iraq," Crocker said, speaking in Arabic during a visit to the Shiite holy city of Najaf, south of Baghdad. "Also there is no Iraqi demand in this connection."

Associated Press writer Sinan Salaheddin contributed to this report.