Taleban soldiers are still patrolling Kabul
The Taleban ambassador to Pakistan told Reuters the "horrendous terrorist attacks" had killed at least 20 people across the country.
During the night there were also reports of heavy artillery and rocket exchanges on the frontline just north of Kabul, where the opposition Northern Alliance is reported to be gearing up for a major offensive.
Following Sunday's air strikes the UN has halted all food convoys into Afghanistan indefinitely.
World Food Programme spokeswoman Christiane Berthiaume said: "We have suspended the operation. Everything has been put on hold because of what happened overnight."
She did not know when operations would resume.
Millions of Afghans depend on international aid to survive.
The WFP decision came after the American military dropped food aid into Taleban-held parts of Afghanistan during the air attacks.
US Defence Secretary Donald Rumsfeld said 37,500 ration packs had been parachuted in.
Fears are also growing for the safety of British journalist Yvonne Ridley and eight foreign aid workers being held by the Taleban.
The Taleban cabinet called an emergency meeting in Kabul to discuss the crisis.
Taleban officials said three people died in air raids on their southern stronghold of Kandahar.
The US-led strikes came nearly a month after suicide attacks on New York and The Pentagon left more than 6,000 people dead.
America's chief suspect is Saudi-born cleric Osama Bin Laden, being protected in Afghanistan by the Taleban regime.
'Morale boosted'
After Sunday's air strikes, Afghanistan's official Voice of Shariat radio said that Kabul had not suffered any casualties or damage and that the Taleban's morale was boosted.
The Taleban said Bin Laden was safe, as was its spiritual leader Mullah Mohammad Omar.
When asked if the two were alive, the Taleban Ambassador to Pakistan Mullah Abdul Salam Zaeef said: "Thanks be to God."
He told Reuters that houses near Kabul airport were hit and women and children were killed.
Mosques in Kabul opened for early morning prayers and calls were made for a jihad [holy war] against America.
"We have to sacrifice ourselves for our country and Islam," was one call.
Afghan Islamic Press, based in the Pakistani city of Peshawar, reported that 10 people were killed near Kabul airport and another 10 died when a bomb fell near the Voice of Shariat radio station.
As dawn broke in Kabul, frightened residents began emerging from their homes.
One resident told Reuters: "Only God knows what has happened. I am leaving. I will sleep under the sky rather than stay in the city for another night."
Too frightened to stay
An elderly disabled man at a bus station said he was too frightened to stay in a city that has seen large areas reduced to rubble in more than 20 years of war.
"We are leaving because it is no longer safe here - thanks to America," he said.
However, many were getting on with normal daily life, opening their shops.
Taleban guards were said to be in their normal positions outside government offices.
Opposition gears up
In the wake of the US-lead attacks, anti-Taleban forces were preparing for a major offensive.
Touryali Ghiasi, a senior strategist for the Northern Alliance, told the Associated Press: "We are in a state of absolute readiness. We are preparing to move."
He said he understood that the Taleban's ministries for defence, information and interior were destroyed in Kabul. Also, the key Darulaman military base west of the city was hit, he said.
There is no word on the safety of eight aid workers in Kabul - four Germans, two Americans and two Australians - who were arrested in August on charges of trying to convert Muslims to Christianity.
British journalist Yvonne Ridley had been arrested by the Taleban for entering Afghanistan illegally, but reports before Sunday's air strikes said she was to be released.