US and Iraqi forces control fewer than one-third of Baghdad's neighbourhoods, according to a review of a security crackdown in the city since February.
Near daily bombings cause misery in many flashpoint districts
An interim US military assessment says sectarian violence has diminished in some areas, but is particularly serious in Sunni-Shia areas of west Baghdad.
More than 20,000 US reinforcements are being deployed as part of the campaign.
Details of the report came as police said they had shot a suspected female suicide bomber in east Baghdad.
An interior ministry spokesman said the woman in traditional Muslim dress, walked towards a police recruiting centre and ignored calls to stop.
Three police recruits received minor wounds from the explosion. The woman died at the scene of the attack.
"Some elements of the mechanised brigade saw a suspicious woman and ordered her to stop, but she didn't respond and approached the recruits, so they opened fire on her and she exploded," a police spokesman said.
Although suicide bombings are a frequent occurrence in Iraq, female bombers are relatively rare.
A US military spokesman said it would not be possible to judge the success of the Baghdad security plan until all the extra units had been put in place.
"It's going to get harder before it gets easier," Lt-Col Christopher Garver said. "We know it's going to be a tough fight over the summer."
Details of the interim assessment included information that US and Iraq forces were in control of just 146 of Baghdad's 457 districts.
The clampdown is meant to allow a window for reconciliation
The report highlighted a failure of Iraqi police and army units to provide all the forces promised to carry out basic security tasks including manning checkpoints and conducting patrols.
May had the third highest death toll of American soldiers, 127, since the US-led invasion to overthrow the government of Saddam Hussein in March 2003.
Thousands of Iraqis have been killed since February.
Correspondents say there was a significant reduction in the number of sectarian killings early on in crackdown, but numbers have now risen again, with dozens of bodies being found in Baghdad almost every day.
President George W Bush won a tough battle with opposition-controlled Congress to fund the crackdown and is under pressure to show progress or start bringing troops home.