Anthrax attacks and a flu vaccine shortage troubled the first and last years of Tommy Thompson’s tenure as Health and Human Services secretary. A much brighter note, he said Friday, was the Medicare prescription law he helped pass in 2003.

Thompson, 63, announced his resignation Friday, saying he was likely to pursue a job in the private sector after nearly 40 years in politics and government.

‘‘We touched the third rail of politics and delivered on our promise to modernize Medicare with prescription drug coverage,’’ Thompson said.

The Medicare law has been bitterly debated, both before and after its passage, with critics contending it showers money on insurers and drug makers at the expense of older Americans.

Despite that criticism, however, Thompson won praise Friday from Sen. Edward M. Kennedy, D-Mass., who said the secretary ‘‘was always willing to try to tackle issues objectively.’‘

Thompson had been the nation’s longest-serving governor when Bush named him to lead the department. He made his mark as governor by pushing for an overhaul of Wisconsin welfare laws, well before Congress and President Clinton took up the issue on the national level.

But a month after the Sept. 11 attacks, the nation faced its first case of bioterrorism in the form of anthrax attacks against government and media targets in Washington, Florida and New York.

Thompson generally escaped criticism, but lawmakers complained that the Centers for Disease Control and Prevention reacted slowly to the crisis.

This year, similar criticism has been leveled at the Food and Drug Administration for its reaction to the loss of half the U.S. supply of flu vaccine because of contamination at a manufacturing plant in England.

The FDA also has come under fire for its handling of safety concerns about Merck & Co.‘s Vioxx painkiller.

Thompson, meanwhile, has been a key player in President Bush’s AIDS initiative, a commitment of $15 billion over 5 years for treatment and prevention of the scourge overseas.

He traveled frequently to Africa and is chairman of the Global Fund to Fight AIDS.

Thompson has used his AIDS role to trumpet his idea of medical diplomacy, investing in health care and medical facilities around the world.