The strikes opened what Pentagon and military officials said would be a week-long bombing campaign by supersonic jets from aircraft carriers and heavy bombers flying from as far away as Missouri.
In a sign of the intensity and duration of the planned campaign, the US B-2 stealth bombers did not return to their hangars at Whiteman Air Force Base after striking their targets, but flew to Diego Garcia, in the Indian Ocean, to reload for more bombing runs.
It is the first time the sophisticated, bat-winged B-2s, built at a cost of $US2 billion each, have been based overseas for a combat mission.
President George W. Bush said Afghanistan's fundamentalist Islamic rulers were paying the price for supporting terrorism and sheltering Osama bin Laden, suspected mastermind of the suicide strikes on the World Trade Center and the Pentagon that killed about 5600 people.
While the sophisticated US and British weaponry is expected to meet little resistance, uneasy allies in the war against terrorism await an "anytime, anywhere" response from a terrorist network which stretches to more than 60 countries.
In a chilling, pre-recorded video riposte to the strikes, bin Laden called on every Muslim to rise to defend his religion.
"The war against Afghanistan and Osama bin Laden is a war on Islam," he said in the video broadcast by Qatar's Al-Jazeera network.
" ... I swear by God the Great that the United States will never taste security and safety unless we feel security and safety in our land of Palestine."
The US State Department issued a worldwide caution warning on the possibility of "strong anti-American sentiment and retaliatory actions against US citizens and interests throughout the world".
At US airports and sports stadiums, state capitols and downtown office buildings, and on the streets from Utah to New York, authorities stepped up already heightened patrols and security precautions.
Many Americans have been buying gas masks and antibiotics, fearing attack by chemical or biological weapons. The number of possible targets are endless, from nuclear power plants to crowded subway trains.
Americans and Britons in Indonesia - where Muslim extremists have threatened to retaliate - were warned to stay indoors, as armoured personnel carriers assembled in the capital, Jakarta.
Americans in Malaysia were under police protection as the Islamic opposition party labelled them "war criminals" and appeared to back calls for a holy war.
Security was tightened at airports and public buildings in Australia, which has offered its forces to the US-led campaign.
More New Zealanders cancelled plans to travel to America, Europe and Asia.
"There will be more strikes by terrorists against US interests; whether it's here or abroad or both, remains to be seen," one US official said.
"There is little doubt that they are going to do something. They have been killing Americans for a number of years and were going to continue doing it whether we did this or not."
At the White House, President Bush said Operation Enduring Freedom was initially designed to disrupt the use of Afghanistan as a terrorist base and attack the military capability of the Taleban.
"Initially the terrorists may burrow deeper into caves and other entrenched hiding places. Our military action is ... to drive them out and bring them to justice."
There were reports of heavy artillery and rocket exchanges during the night on the frontline just north of Kabul, as the Northern Alliance opposition took advantage of the air strikes.
The US-led attacks on military bases, airports, guerrilla training camps and Taleban command centres around Kabul, Kandahar and Jalalabad were accurate, but resulted in casualties, witnesses reported.
A spot check of four hospitals in Kabul turned up no evidence of casualties.
But Kabul's airport was closed and some families, especially those living near the airport or other targets, were on the move. Mirza Mohammed was preparing to leave with his four children. He was bound for Logar province in the central part of Afghanistan.
"We were very afraid. We didn't sleep," said Mohammed, who lives near the airport on the northern edge of Kabul.
I haven't seen Osama bin Laden in my life," he said. "I don't understand why the people of Afghanistan are such unlucky people."
In a stick-and-carrot strategy, US planes also dropped leaflets calling on the Taleban to end their resistance, and aircraft loaded with food supplies dropped 37,500 humanitarian food packages into remote areas to help feed thousands of displaced refugees.
Bush claimed the "collective will of the world" was backing the attacks.
More than 40 countries in the Middle East, Africa, Europe and Asia had granted the use of their airspace or landing rights. British forces took part in the operation, and Canada, Australia, Germany and France have pledged forces as the operation unfolds.
Pakistan, the only state still to recognise the Taleban as a legitimate government, said the regime had brought the strikes on itself.
Clean-up workers at the World Trade Center site reacted with support and a sense of justice to the news, and fans at football and baseball stadiums burst into cheers.
"It's big-time payback," said Charles Rios, 38, a worker helping with the clean-up. "I'm so happy now."
But condemnation came from Iraq, Iran and the Palestinian Hamas movement responsible for a series of suicide bombings against Israeli civilians.
Police using teargas broke up several protests in the Pakistan border city of Peshawar as angry students tried to demonstrate against the attacks.
