The two men are to appear on Capitol Hill again on April 8 and 9.

These more frequent reviews are advocated, officials said, by the Joint Chiefs of Staff and by the military’s Central Command, which is responsible for operations across the region, including those in Afghanistan. The reviews would determine how many more brigades, if any, could be ordered out of Iraq in the final months of the Bush presidency.

Reducing the troops in Iraq as much as is feasible has been a priority of the Joint Chiefs of Staff, who are to brief Mr. Bush this week. The Joint Chiefs have argued in favor of finding ways to ease the strain of the war in Iraq on military training and morale and to balance General Petraeus’s plans for Iraq with the need to prepare for other potential conflicts. A decision to suspend further reductions has already prompted criticism from Democrats in Congress, especially as the presidential primary campaign has intensified.

The two Democratic candidates, Senators Hillary Rodham Clinton and Barack Obama, have proposed more rapid withdrawals of troops, though on different timelines. The Republican candidate, Senator John McCain, has advocated following a policy close to that of President Bush’s.

Mr. Bush on Monday addressed the milestone of the 4,000th death during a brief statement at the State Department, where he met with Secretary of State Condoleezza Rice and other senior aides. In a statement that began haltingly, he expressed his sympathies for the families of those killed, both soldiers and diplomats, and sought to put their deaths in historical context.

“I have vowed in the past, and I will vow so long as I’m president, to make sure that those lives were not lost in vain; that, in fact, there is a outcome that will merit the sacrifice that civilian and military alike have made; that our strategy going forward will be aimed at making sure that we achieve victory,” he said.

By many accounts, the addition of five combat brigades last year, which raised the American troop level to a peak of nearly 170,000 from 132,000, was a factor in helping reduce violence in Iraq. But Mr. Bush and his aides are described as wary of risking the gains.

Mr. Bush, according to officials, could decide to make no further reductions in troops after the departure this summer of the last of the additional troops, leaving roughly 140,000. That number includes the 15 combat brigades in Iraq before the troop increase, as well as additional support, training and other units that are expected to stay.