The first daylight raid came hours after dawn today, when jets bombed the southern city of Kandahar.
The U.S. strikes yesterday were slightly less heavy than the barrage launched Sunday in response to the terrorist attacks on the United States, officials said.
The targets, though, were similar. They included Taliban anti-aircraft positions that could endanger U.S. planes taking part in bombing runs and dropping humanitarian food rations for Afghan civilians.
At the White House, President Bush said the military strikes had been "executed as planned" and added:
"This will be a long war. It requires understanding and patience from the American people."
With American bombs dropping overseas and many people fearful of terrorist reprisals at home, Attorney General John Ashcroft outlined precautionary steps the government has taken, including tightened security at nuclear facilities and power plants.
Authorities said a second case of anthrax exposure was discovered in someone who worked in the same Florida building as a man who died last week of inhalation anthrax, an extremely rare and deadly form of the disease.
The FBI is looking into the possibility that the two cases were the result of terrorism or criminal action.
"It is a source of concern," said Ari Fleischer, the White House spokesman.
Yesterday, Western reporters in Afghanistan said anti-aircraft gunfire could be heard around Kabul, the Afghan seat of government, and Kandahar, considered the country's spiritual capital. U.S. forces also hit Taliban positions near the northern city of Mazar-e Sharif, Pentagon officials said.
The Pentagon said five long-range bombers, 10 sea-launched warplanes and 15 Tomahawk cruise missiles struck an undisclosed number of targets, including early-warning radars and Taliban ground forces.
Defense Secretary Donald H. Rumsfeld said the initial round of bombing had succeeded at least moderately in striking the Taliban's air defenses, airfields and aircraft. But Rumsfeld also sought to lower any expectations for a military rout, saying it was unclear whether the U.S. strikes had destroyed command centers and other military facilities.
"That country has been at war for a very long time. The Soviet Union pounded it year after year after year. Much of the country is rubble. They have been fighting among themselves. They do not have high-value targets that would lend themselves to substantial damage from the air."
As law enforcement authorities guarded against possible terrorism, Tom Ridge was sworn in as director of a new White House Office of Homeland Security. With Bush at his side, Ridge pledged to foster a spirit of coordination among the many federal agencies that deal with counter-terrorism and to help close gaps in the nation's security systems.
The former Pennsylvania governor said the size and scope of his mission were "difficult but not impossible." Though critics have warned that he will lack the budgetary authority to do much more than provoke turf wars among agency chiefs, Ridge declared, "The only turf we should be worried about protecting is the turf we stand on."