The US military in Iraq says it has detained 32 suspected militants in a series of overnight raids.
An extra 20,000 US troops are being deployed as part of the "surge"
Some 16 were seized in Sadr City in Baghdad, a stronghold of Shia militias where US and Iraqi troops have been searching for five abducted Britons.
In north-western Iraq, at least nine people died in a suicide truck bomb attack on a police post in Rabia.
The new spokesman for the US military in Iraq has defended the recent "surge" in troops aimed at tightening security.
The US military said the men detained overnight were suspected members of a network involved in bringing sophisticated bomb components into Iraq from Iran.
Others were held in raids targeting al-Qaeda fighters around Falluja and Hit, west of Baghdad.
The British ambassador to Iraq has appealed for the release of the five Britons kidnapped in Baghdad last week.
"We have people here in Iraq who are ready to listen to any person about this incident, or any person who may be holding these men and who may wish to communicate," Dominic Asquith told reporters.
In the Rabia attack, which took place in the town near Iraq's border with Syria, the police station targeted was flattened and 22 people were injured. Four policemen were reported to be among the dead.
The US new military spokesman in Iraq, Brig-Gen Kevin Bergner, said troops were still being deployed, and it would take some time for the new force to become fully effective.
But he denied that the operation was failing.
"Sectarian killings, while there might have been a bump up in the month of May, the overall trend since we began this operation in January has seen some improvement," he told the BBC's Today programme.
"You know from having followed this for a while, the nature of progress in Iraq is not a linear one. It's uneven, you have progress and you have setbacks."
He defended the government of Iraq, which he said was trying to wrestle with normal issues such as wealth distribution and power sharing in a difficult security situation.
"When you see all of that taking place here it has a little bit of a different context than when you look at it perhaps from afar," he said.
"No question, though, that this government still has a great deal of work to do ahead of it and there are still many things that it must sort out before it can have the kind of reach and the kind of enduring nature that our governments have now achieved after a long time as democracies."
More than 20,000 US reinforcements are being deployed as part of the surge.
May had the third-highest death toll of US 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 the crackdown, but numbers have now risen again, with dozens of bodies being found in Baghdad almost every day.