The White House said Powell, Veneman, Paige and Abraham would remain until their successors were confirmed.
"That's the typical D.C. speculation game that people like to engage in, no matter how wrong it is," the press secretary said.
Yet despite the president's praise, Powell's cautious approach — especially regarding the use of military power — often was rejected.
Powell's reputation was somewhat tarnished within the foreign policy community when, during the run-up to the Iraq war, he went before the United Nations and offered what he said was clear proof that Saddam Hussein had weapons of mass destruction — proof that turned out to be based on flawed intelligence.
The resignations announced Monday were the latest in what will likely be a continuing exodus. Last week, in addition to Ashcroft, Commerce Secretary Don Evans announced that he intended to leave.
Bush has named White House Chief Counsel Alberto R. Gonzales to take over for Ashcroft at the Justice Department. McClellan said White House Chief of Staff Andrew H. Card Jr., who Bush has announced will remain for a second term, was heading up the process of developing other job candidates.
Although several of President Clinton's Cabinet secretaries served the full eight years, the average tenure in recent history has been less than three years, said G. Calvin Mackenzie, a professor at Colby College in Maine who specializes in presidential appointments.
Mackenzie said one challenge facing Bush was to come up with Cabinet nominees who would not get entangled in partisan Senate confirmation battles. He predicted that at least some of the replacements would be officials now serving in the White House or in other government agencies, rather than high-profile outsiders.
Such officials can make appealing candidates because their strengths and weaknesses are known, and they provide policy continuity.
Towson University political scientist Martha Joynt Kumar said that Bush seemed to be moving quickly to assemble his second-term Cabinet so that attention could be focused on the administration's policy agenda instead of personnel, as occurred during the lull between Clinton's first and second terms.
"Their intention is to appoint their people by Thanksgiving. In the Clinton administration it was to do so by Christmas," Kumar said. "Even though it's only a month's difference, it provides an opportunity to command the stage during a period when no one else in Washington is talking."
But Paul Light, a professor of public service at New York University, warned that it may take significantly longer to fill an array of "sub-Cabinet" posts that were likely to become vacant as well.
Other Cabinet secretaries who may resign soon, according to Washington insiders, include Homeland Security Chief Tom Ridge; Health and Human Services Secretary Tommy G. Thompson; U.S. trade representative Robert B. Zoellick; Labor Secretary Elaine Chao; and Transportation Secretary Norman Y. Mineta, the only Democrat in Bush's Cabinet.
Abraham leaves the Energy Department after a tenure marked by frustration. Despite Republican majorities in both the House and Senate, the administration failed to win congressional approval of Bush's high-priority energy bill, which emphasized increased conservation but also increased energy production — including drilling in Alaska's Arctic National Wildlife Refuge.
Although Abraham, 52, a former Michigan senator, received mixed reviews as a salesman for Bush's initiatives, some analysts said his role was overshadowed by the vice president's involvement in formulating energy policy behind closed doors.
Abraham "shepherded Bush's energy plan as well has he could," said Philip K. Verleger Jr., an energy economist at the Institute for International Economics in Washington. "Cheney set the energy policy."
Possible successors are said to include retiring Democratic Sen. John B. Breaux, a moderate from energy-rich Louisiana; Edison Electric Institute President Thomas Kuhn, who was a Bush classmate at Yale, and U.S. Ambassador to Mexico Tony Garza, a former Texas energy regulator.
As Agriculture secretary, Veneman, 55, led a sprawling agency with more than 100,000 employees and an annual budget exceeding $80 billion.
The daughter of a California peach grower, she headed the California Department of Food and Agriculture from 1995 to 1999.
Seen as an able farm trade negotiator and a loyal promoter of the president's policies, Veneman was widely praised for the administration's rapid response to the first reports of mad cow disease in the United States. But she also has drawn criticism for her role in the development of massive farm subsidy legislation that has undermined U.S. credibility in global trade talks.
One potential Veneman successor is said to be Rep. Charles W. Stenholm (D-Texas), a moderate who lost his reelection bid this month after 13 terms.
Other potential replacements include Agriculture Undersecretary William T. Hawks, U.S. agriculture trade negotiator Allen Johnson, White House agriculture advisor Chuck Conner, Agriculture Department conservation chief Bruce Knight, and Missouri Farm Bureau President Charles Kruze.
Paige, 71, the first African American to serve as the nation's top education official, is best known for his role in promoting the president's No Child Left Behind initiative, which imposed testing and accountability standards on elementary and middle schools.
Times staff writer Mary MacVean contributed to this report.