KABUL, Afghanistan — A lone jet screamed through Kabul's early dawn sky Tuesday and dropped a single bomb near the airport on the north side of the city. Shortly afterward a missile streaked into the eastern edge of the capital.

Taliban anti-aircraft gunners replied with a quick burst of fire.

The fresh assault at 6:50 a.m. rattled windows in the capital and awakened sleeping residents who had passed a quiet night after a second wave of U.S. strikes Monday evening.

Heavy bursts of anti-aircraft fire had ripped the night sky over a darkened Kabul Monday night, and the Taliban militia responded to the second U.S. barrage by cutting power and ordering residents to shutter themselves indoors.

At least three bomb explosions had reverberated through the capital — one each in the eastern, western and northern sections of the city. A high-flying plane could be seen dropping flares before the detonations. Taliban gunners responded with a crackle of fire into the skies over the city.

Targets in Monday's raids included areas around the capital, the Taliban's home base of Kandahar, and Afghanistan's north, where an opposition northern alliance is battling the Taliban, the Islamic movement that controls nearly all of Afghanistan.

The military campaign is aimed at punishing the Taliban for harboring Osama bin Laden, the man accused of plotting the Sept. 11 attacks on New York and Washington that left more than 5,500 people dead or missing.

The Afghan Islamic Press agency in Islamabad, Pakistan, said the airport in Kabul and a hill where a TV transmission tower is located were both targets.

The agency, which has close ties to the Taliban, said one bomb landed near a 400-bed women's hospital in Kabul but made no mention of any damage. The reports could not be independently confirmed because a curfew is in effect in the Afghan capital.

Lights went out in Kabul soon after the attack began, and Taliban radio ordered people to close their blinds, shut off lights and stay indoors.

Taliban positions around the northern city of Mazar-e-Sharif were also under attack Monday, the Afghan press agency reported. Ashraf Nadim, a spokesman for the opposition northern alliance, said by telephone that his forces were tipped off by the United States a half hour before Monday's attacks.

Nadim, speaking from Samangan province, about 30 miles from Mazar-e-Sharif, said U.S. aircraft and missiles were launched against Taliban positions there.

The Afghan press agency said the northern alliance launched a major attack Monday evening on the Taliban position near Dara-e-Suf, in northern Samangan.

In Washington, Defense Secretary Donald H. Rumsfeld suggested there was much left to do after the first night's aerial assault. ``We believe we've made progress toward eliminating the air defense sites,'' he said. ``We believe we've made an impact on military airfields. ... We cannot yet state with certainty we have destroyed'' dozens of command and control and other military targets,'' he said.

Air Force Gen. Richard Myers, chairman of the Joint Chiefs of Staff, said the fresh bombardment Monday night was accompanied by a renewed air drop of humanitarian assistance.

Five long-range bombers — a pair of B-2 stealth bombers flying from Whiteman Air Force Base, Mo., and three B-1B's from the Indian Ocean island of Diego Garcia — joined 10 strike planes launched from aircraft carriers in the Arabian Sea. They targeted air defense and other military targets across Afghanistan.

Two U.S. Navy ships, the destroyers USS John Paul Jones and USS McFaul, and one submarine launched a total of 15 Tomahawk cruise missiles.

Britain, which participated in the first wave of assaults on Sunday, did not take part in Monday's follow-up, Prime Minister Tony Blair said from London.

Before Monday's attacks began, President Bush vowed to be ``relentless'' in fighting terrorism ``on all fronts.''

In an indication the United States might want to some day expand the military operation, Washington formally notified the U.N. Security Council on Monday that counterterrorism attacks may be extended beyond Afghanistan.

The first night of strikes Sunday targeted Kabul, Kandahar, Mazar-e-Sharif and Jalalabad, a city along the Pakistani border. The compound of Taliban leader Mullah Mohammed Omar in Kandahar, as well as training bases of bin Laden's al-Qaida terrorist network, were also hit.

Taliban radio on Monday derided the previous night's strikes as a failure. ``The American bombardment and rocket attacks didn't hit their targets,'' it said.

Shortly after the first attacks Sunday, bin Laden vowed in an apparently pre-taped message that America will ``never dream of security.'' He praised God for the Sept. 11 attacks and said the United States ``was hit by God in one of its softest spots.''

Taliban officials said both he and Omar survived the first night's assault. There was no word from the Taliban on Monday's second strike.

Before the night assault Monday, the Taliban released a British journalist and handed her over to Pakistani authorities, border officials said. Yvonne Ridley, a reporter for a London tabloid, had been arrested in Afghanistan 10 days earlier, after all foreigners were ordered out of the country. The militia is still holding eight foreign aid workers — including two Americans — accused of trying to convert Muslims to Christianity.

Washington called the airstrikes that began Sunday night a success, saying military installations and terrorist training camps were prime targets.

Meanwhile, neighboring Pakistan on Monday carried out its second government reshuffle in as many days, replacing its secret service chief, who had failed to convince the Taliban to hand over bin Laden.