Bush was to participate in a two-hour conference by secure video hookup with Gen. David Petraeus, the top commander in Iraq, and Ryan Crocker, the U.S. ambassador to Iraq. Petraeus and Crocker are due to testify in Congress on April 8-9.
Petraeus is expected to recommend no additional troop reductions in Iraq beyond those already scheduled, until at least September. This so-called pause in drawdowns, lasting a month or two, would be designed to assess the impact of this round, with the expectation that the drawdown would resume before Bush leaves office in January.
White House press secretary Dana Perino said Bush sees "some merit" in that idea. "I think that's not unlikely," she said. She said Bush is under "no deadline" to make a decision about troop levels before leaving next week for a NATO summit in Romania.
Perino said that Bush spends time every day thinking about those who have lost their lives in battle.
"He bears the responsibility for the decisions that he made," Perino said. "He also bears the responsibility to continue to focus on succeeding."
Perino said families of the fallen soldiers often tell the president that they want him to complete the mission in Iraq.
With the war entering its sixth year, Bush makes the argument that defeating extremists in Iraq makes it less likely that Americans will encounter enemies at home. Iraq has taken a heavy toll on his presidency, contributing to Bush's low poll ratings.
Perino, though, said that the security gains of the past year have been important to stabilizing Iraq.
Bush also is to receive briefings Monday at the State Department and on Wednesday at the Pentagon "on what actions his advisers recommend for cementing those gains and taking action that will lay the foundation for further additional troop drawdowns," Perino added.
A roadside bomb killed four U.S. soldiers in Baghdad on Sunday, the military said, pushing the overall American death toll in the five-year war to at least 4,000. The grim milestone came on a day when at least 61 people were killed across the country.
Rockets and mortars pounded the U.S.-protected Green Zone, underscoring the fragile security situation and the resilience of both Sunni and Shiite extremist groups despite an overall lull in violence.
The soldiers with Multi-National Division - Baghdad were on a patrol when their vehicle was struck at about 10 p.m. in southern Baghdad, the military said. Another soldier was wounded in the attack.
Identities of those killed were withheld pending notification of relatives.
The president had no scheduled comments about the war on Monday.
Vice President Dick Cheney, in Jerusalem to push the Mideast peace process, said the 4,000th American death in Iraq may have a psychological impact on the American public.
"You regret every casualty, every loss," he said. "The president is the one that has to make that decision to send young men and women into harm's way. It never gets any easier."
In Baghdad, U.S. soldiers told CBS News chief foreign correspondent Lara Logan that they don't count the number of soldiers killed. Every single death is hard for them.
The leader of the House of Representatives, Speaker Nancy Pelosi, a Democrat, said Americans are asking how much longer their troops must sacrifice for an Iraqi government "that is unwilling or unable to secure its own future."
"Americans also understand that the cost of the war to our national security, military readiness and our reputation around the world is immense and that the threat to our economy as the war in Iraq continues to take us deeper into debt is unacceptable," Pelosi said.
Commenting on the 4,000 deaths, Perino said, "President Bush believes that every life is precious, and he spends time every day thinking about those who've lost their lives on the battlefield. He grieves for the families who have lost loved ones, and he is constantly concerned about their well-being."
"The president has said the hardest thing a commander in chief will do is send young men and women into combat, and he's grieved for every lost American life, from the very first several years ago to those lost today," the press secretary said.
The U.S. has about 158,000 troops in Iraq. That number is expected to drop to 140,000 by summer in drawdowns meant to erase all but about 8,000 troops from last year's increase.
Sen. Hillary Rodham Clinton, vying for the Democratic presidential nomination, told a campaign audience in the state of Pennsylvania that she would honor the fallen by ending the war and bringing home U.S. troops "as quickly and responsibly as possible." Her rival for the nomination, Sen. Barack Obama, said "It is past time to end this war that should never have been waged by bringing our troops home, and finally pushing Iraq's leaders to take responsibility for their future."