Bodies lay scattered across two central Baghdad neighborhoods Wednesday after a raging battle that left 20 insurgents and four Iraqi soldiers dead, and 16 U.S. soldiers wounded, witnesses and officials said.

The fighting in Fadhil and Sheik Omar, two Sunni enclaves, was the most intense since a massive push to pacify the capital began two months ago.

Iraqi soldiers held a security cordon around Fadhil on Wednesday, and residents hid frightened in their homes, a witness told The Associated Press by telephone, on condition of anonymity out of fear for his safety.

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The Muslim Scholars Association, a Sunni group, issued a statement quoting witnesses as saying Tuesday's battle began after Iraqi troops entered a mosque and executed two young men in front of other worshippers. Ground forces used tear gas on civilians, it said.

"The association condemns this horrible crime carried out by occupiers and the government," the statement said.

But the witness in Fadhil said the two men were executed in an outdoor vegetable market, not in the mosque. The Iraqi military was not immediately available to comment on the claim.

The U.S. military said the battle began after American and Iraqi troops came under fire around 7 a.m. during a routine search operation. Helicopter gunships then swooped in, engaging insurgents with machine gun fire, the military said in a statement.

Some Arab television stations reported an American helicopter was shot down in the fight, and showed video of a charred piece of mechanical wreckage that was impossible to identify. The U.S. said an attack helicopter suffered damage from small arms fire but returned to base.

A senior U.S. military official said that by Wednesday, 13 of the 16 wounded Americans had returned to duty. Twenty insurgents were killed and 30 wounded, he said.

Baghdad's security crackdown, which began Feb. 14 and will see nearly 170,000 American forces in Iraq by the end of May, has curbed some sectarian attacks and assassinations in the capital. But violence continues to flare periodically and has risen markedly in nearby cities and towns.

In other violence Wednesday, a roadside bomb killed one policeman and wounded three others in Hillah, about 95 kilometers (60 miles) south of Baghdad, police said.

Another roadside bomb targeted a police patrol in Mosul, 225 miles northwest of Baghdad, killing another policeman and wounding two others, police said. Six civilians were also hurt, said Brig. Abdul Karim Khalaf.

On Tuesday, a woman with a suicide vest hidden under her black Muslim robe blew herself up in a crowd of about 200 Iraqi police recruits in Muqdadiyah, 60 miles north of Baghdad.

The attack killed at least 16 people and wounded 33, said Dr. Abdul Salam al-Jibour at Muqdadiyah General Hospital.

Most of the victims had taken police exams just days earlier and were assembled to learn the results, said a policeman, who would not give his name because he was not authorized to talk with reporters.

Complete coverage is available in FOXNews.com's Iraq Center.