FALLUJAH, Iraq — Defense Secretary Gates slipped into Iraq yesterday to warn Iraqi leaders that the American commitment to a military buildup there is not open-ended.

Mr. Gates said the political tumult in Washington over financing the military presence in Iraq shows that both the American public and the Bush administration are running out of patience with the war.

“I’m sympathetic with some of the challenges that they face,” Mr. Gates said of the Iraqis during his surprise visit. But, he said, “the clock is ticking.”

Mr. Gates added, “Frankly, I would like to see faster progress.”

He said the Iraqis need to push through legislation on political reconciliation and sharing oil revenues. “It’s not that these laws are going to change the situation immediately, but I think … the ability to get them done communicates a willingness to work together.”

He said that, in turn, would create an environment in which violence could be reduced.

Underscoring the urgency in controlling the violence, police said a suicide car bomber rammed into a fuel truck in central Baghdad only hours before Mr. Gates’s arrival, killing at least a dozen people. The attack came a day after one of the bloodiest days in Baghdad since the U.S. troop increase began nine weeks ago, with four strikes killing more than 230 people.

“It is very important they make every effort to get this done as soon as possible,” Mr. Gates said, noting that an attack last week by a suicide bomber on a cafeteria at the Iraqi parliament inside the American-guarded Green Zone made people particularly nervous.

After landing in Baghdad, Mr. Gates flew by helicopter to Camp Fallujah, for a briefing by General David Petraeus, the commander of U.S. forces in Iraq, and General Peter Pace, the Joint Chiefs chairman. Fallujah, where U.S. Marines make up the bulk of the U.S. force, is a stronghold for Sunni insurgents. But commanders there have been saying violence has dipped and they are optimistic about progress in western Iraq.

Mr. Gates, who stopped in Iraq on a trip through the Middle East, also planned to meet with Iraqi political leaders. His visit, the third to Iraq since taking over as defense secretary in December, came a day after Mr. Bush met with congressional leaders to discuss the impasse over legislation to provide funds for the war effort in Iraq and Afghanistan.

Mr. Gates said the White House has not asked him whether there is a compromise on a deadline for withdrawal from Iraq that the U.S. military could accept.

Three of the five brigades ordered into Iraq by President Bush to stem Baghdad violence have arrived, bringing the American forces in the country to 146,000. Officials want the rest in place by June, for a total of 160,000.

Soon after that they plan to assess how much longer the higher troop level — about 30,000 more than before the buildup — will be needed.

Officials have struggled to find troops from within the stretched U.S. military. Mr. Gates last week took the difficult step of lengthening tours of duty to the war zones in Iraq and Afghanistan to 15 months from a year.

During an hour-long meeting Wednesday at the White House, the president told lawmakers directly he will not sign any bill that includes a timetable for troop withdrawal, and they made it clear Congress will send him one anyway.

“We believe he must search his soul, his conscience and find out what is the right thing for the American people,” the Senate majority leader, Senator Reid of Nevada, told reporters after the session. “I believe signing this bill will do that.”