Britain's Ministry of Defense said it is sending two additional battalions to Iraq, adding 1,200 troops to its 11,000-man force on the ground.
Earlier Monday, Iraqi guerrillas attacked an American patrol in Baghdad with explosives as soldiers were driving out of a tunnel in the center of the city, the military said.
The attack wounded two soldiers, damaged two Humvees, one of which turned over and caught fire, according to a military spokesman.
Just hours before President Bush, in a nationally televised address, said he would ask Congress for $87 billion to cover military and reconstruction work in Afghanistan and Iraq. He called Iraq the "central front" in the war on terror.
The U.S. administrator for Iraq, L. Paul Bremer promised the United States would not leave Iraq before its mission was complete.
"This is one of the largest nonmilitary budgets requested in American history," Bremer said. "It amounts to more than 10 times more than the United States has ever spent in a year in any country.
"And it's a clear, dramatic illustration of the fact that the American people are going to finish the job we started when we liberated Iraq some four months ago," the 61-year-old former counterterrorism expert said.
In other developments:
Despite calls from Republicans and Democrats alike for more troops, Mr. Bush said the 130,000 U.S. forces in Iraq were sufficient. But he urged other nations, even those that had opposed the war, to contribute troops and money.
The president addressed the nation Sunday night, his first speech on Iraq since May 1 when he stood on the aircraft carrier Abraham Lincoln and declared an end to major combat.
In the four months since, U.S. casualties have risen steadily, to the point where more have died in the aftermath of the war than during the combat phase.
U.S. allies were reacting cautiously to the call for more foreign help. Japan, normally a quick backer of Washington, offered only a lukewarm response and other nations said they would like to see greater United Nations involvement in post-war Iraq first.
Britain has been weighing new troop deployments for weeks.
Some 120 servicemen were sent to Iraq from Cyprus over the weekend. The Ministry of Defense said they were included in the 1,200 troops whose deployment was announced Monday.
"This response is not a knee-jerk response to recent attacks. It's part of a strategic plan to achieve the goals I have set out," Prime Minister Tony Blair's official spokesman said.
The spokesman, briefing reporters on condition of anonymity, characterized the deployment as "a targeted response to achieve these objectives with one clear objective in mind, and that's to put the Iraqi people in charge of their own areas at national level, as they are in 90 percent of towns and cities."
Eleven British troops have died in Iraq since May 1.
U.S. forces claimed small successes on the ground. The military says it's captured a suspected Saddam loyalist who's accused of having carried out a grenade attack last month that killed three soldiers, and uncovered a stockpile of weapons and ammunitions in Tikrit that included wire-guided surface-to-surface missiles.
The military says a coalition aircraft came under fire from two surface-to-air missiles as it left Baghdad International Airport.
Meanwhile, the Dubai-based satellite channel al-Arabiya has aired a tape by an alleged al Qaeda financier. The voice on the tape aired Sunday denied al Qaeda was involved in the Najaf bombing that killed Iraq's top Shiite Muslim cleric. The person said the terror group's aim is to fight and kill Americans.