Citing estimates from the World Health Organization, Thompson said that as many as 70 million people worldwide could die in a major flu outbreak. Of about 40 known cases of avian flu in humans so far, about 30 have been fatal.
"No other disease has had that kind of lethality before," he said. "And we do not have a vaccine. This is really a huge bomb out there."
He said he worried "every single night" that terrorists would poison food supplies and was amazed they had not done so.
"It is so easy to do," he said. "We're importing a lot of food from the Middle East, and it would be easy to tamper with that."
At the Pentagon, Rumsfeld agreed to stay on after being asked to do so by President Bush, an administration official said. The President's endorsement was a rebuke to critics, including some within the administration, who blame Rumsfeld for many of the problems in Iraq.
Detractors say Rumsfeld failed to provide sufficient troops for the invasion and had no clear plan to secure the peace. An administration official who requested anonymity said Bush believed Rumsfeld was "the right person at this moment in our history in fighting the war on terror to lead our armed forces."
Thompson had long ago signaled his intention to leave after four years of overseeing the agency that he called "America's Department of Compassion."
"It's time for me and my family to move on to the next chapter in our life," he said at the agency's headquarters.
Mark McClellan, the head of the Medicare program and a brother of White House spokesman Scott McClellan, is seen as the top candidate to replace Thompson.
As expected, Bush found a replacement for another departing administration official yesterday, naming former New York Police Commissioner Bernard Kerik to run the Homeland Security Department.
The turnover rate in Bush's cabinet mirrors the experience of other recent two-term presidents, including Bill Clinton, who lost half his cabinet in his second term.
Top government officials traditionally view the start of a second term as a chance to shift to more lucrative, less demanding private-sector jobs. For a second-term president, the personnel changes are an opportunity to bring new life into the administration.
"A number of them have served a full four years now," Scott McClellan said, "and that's a long time for anyone to serve in a position like that. It is also good to have some fresh new faces in place from time to time."
Resignations also are expected from Treasury Secretary John Snow and Transportation Secretary Norman Y. Mineta, the only Democrat in Bush's cabinet.
Thompson faced a host of tough issues during his tenure at Health and Human Services, an agency with a $548 billion annual budget and nearly 67,000 employees.
As a point man for Bush's "compassionate conservatism," Thompson backed welfare programs that encouraged marriage. He lobbied tirelessly for Bush's Medicare overhaul, including the prescription-drug benefit, which begins in 2006. He successfully pushed initiatives to offer more preventive health services under Medicare and to expand the use of electronic medical records.
He opposed stem-cell research and importing prescription drugs from Canada and other countries. He acknowledged being less than thorough in his supervision of a former Medicare administrator, Thomas Scully, who prevented an underling from giving Congress cost estimates for Bush's Medicare prescription-drug plan.
Bush, who got to know Thompson when he was governor of Texas and Thompson was governor of Wisconsin, called him "a true public servant who worked every day to make Americans healthier and to help more Americans in need achieve the dream of independence."
Contact reporter Ron Hutcheson at 202-383-6101 or email@example.com.