Pressure in the United States and Iraq for deadlines comes during a buildup of American and Iraqi troops to buttress the latest security plan for the capital. Three additional American brigades, a total of about 7,000 troops, have already been deployed in and around Baghdad, and two more are scheduled to arrive in the next two months.

The increase appears to have led to a limited reduction in violence in Baghdad, particularly in the kinds of assassinations for which Shiite militias have most often been blamed. But American and Iraqi forces have not been able to stop the car bombings and suicide attacks attributed to the Sunni Arab-led insurgency.

Bridges were the targets of two suicide bombings on Friday in a neighborhood on the southern fringe of Baghdad, killing at least 22 people and wounding at least 50, an Interior Ministry official said.

Military pressure on Baghdad has driven some Sunni Arab militants to Diyala Province, north of the capital, where they have joined a worsening battle between Sunni and Shiite militias.

The challenge to the American and Iraqi military in Diyala was underscored Friday by the American military commander in northern Iraq, Maj. Gen. Benjamin R. Mixon, who said he had asked for more troops to join the fight in the province.

The level of violence in Diyala, already high, has increased since the start of the American-led security crackdown in mid-February, making it one of the most lethal regions in Iraq for American troops.

“I do not have enough soldiers right now in Diyala Province to get that security situation moving,” General Mixon said. “We have plans to put additional forces in that region.” He declined to provide details about possible future deployments. But he insisted that a cornerstone of the country’s long-term security would be a sustained American presence.

“We just can’t think about pulling out of here just like that,” he said.

The American military command said two soldiers were killed and 11 wounded in two attacks on Thursday, one in Baghdad and the other in Diyala. The Interior Ministry official said at least 17 bodies had been recovered from streets around Baghdad.