The attacks came amid warnings that violence will likely increase with fewer than 100 days left before the coalition hands over sovereignty.
A 1st Infantry Division soldier died and two were wounded while they were investigating a report that a homemade bomb had been found near Baqouba, the military said. The two injured soldiers were in stable condition.
The fighting that killed one soldier occurred Wednesday near Taji, 12 miles north of Baghdad, said Brig. Gen. Mark Kimmitt, the U.S. military's deputy director of operations. A U.S. soldier was also wounded.
In other developments:
"One hundred days from now, Iraqis will be sovereign in their own land and responsible for their own future," Bremer said in an outdoor speech in the Green Zone, the heavily protected area housing the coalition headquarters in the center of Baghdad.
Enormous tasks remain before the handover. The biggest involves anointing an Iraqi transitional government that will take power on June 30 — but the Governing Council and U.S.-led occupation figures have yet to agree upon a scheme to name those who will govern.
Bremer announced that he would set up an Iraqi Defense Ministry and a national security Cabinet later this week.
He said he was in the midst of appointing inspectors general to each of Iraq's 25 government ministries while creating a government auditing board and an anti-corruption commission. Bremer said work was under way to establish a public broadcasting service and an independent panel to regulate it.
Bremer already has appointed most Iraqi ministers, many of whom are expected to keep their jobs after the handover. He is currently sorting through the ministers' choices for deputies.
"We're moving at rocket speed," Mouwaffak al-Rubaie, a Shiite Muslim member of the U.S.-appointed Governing Council. "The counting down has started."
But security remains a top concern. U.S. and Iraqi officials expect Iraqi guerrillas and foreign fighters to step up attacks in an attempt to disrupt the handover process and try to demonstrate that a fledgling Iraqi government cannot control the country.
"The security issue cannot be overemphasized," al-Rubaie said.
Kimmitt said the military was worried by attacks on Iraqi police. On Wednesday, the police chief of southern Babil province was shot and killed. A day earlier, nine police recruits were killed in a nearby attack on their vehicle.
"We remain concerned at what is clearly a program of intimidation and targeting of not only the Iraqi police service, but all Iraqi government officials," Kimmitt said. "A significant number of Iraqi police have been killed in the past year, somewhere in the order of 350."
He said that despite the attacks "on almost a daily basis," morale in the force remained high and no significant drop in recruitment or retention rates had occurred.
The soldiers' deaths Wednesday and Thursday brought to at least 584 the number of U.S. service members who have died in Iraq; at least 395 died from hostile action and at least 447 died after Mr. Bush declared major combat over on May 1.
Other countries have suffered 96 deaths. Nearly 3,000 Americans have been wounded.
No official figure exists for Iraqi military of civilian deaths, although the latter have been estimated at more than 3,200.