There was no indication that there was any state sponsorship of today's attacks, the officials said.
Bin Laden warned three weeks ago that his followers would carry out an "unprecedented attack" on the United States, an Arab journalist told Reuters news agency.
Along with several other world leaders, Palestinian leader Yasser Arafat condemned the aircraft attacks. Arafat spoke shortly after an anonymous caller told Abu Dhabi television that a radical Palestinian group was responsible for the attacks. The group later denied any involvement.
"I send my condolences, the condolences of the Palestinian people to American President Bush and his government and to the American people for this terrible act," Arafat told reporters in Gaza. "We completely condemn this serious operation … We were completely shocked. It's unbelievable, unbelievable, unbelievable."
House and Senate leaders stood side by side in a show of unity this evening and vowed to stand together behind the nation and Bush. They said that the acts of terror would not stop Congress from convening Wednesday.
In Kabul, Afghanistan's capital, early Wednesday morning but this evening in Washington, video from a Middle Eastern news agency showed flames, explosions and tracer fire. Bin Laden, considered to be one of the world's most dangerous terrorists, is said to be based in Afghanistan.
White House spokesman Ari Fleischer said the attacks in Kabul were not ordered by the United States. Pentagon spokesman Craig Quigley said: "It isn't us. I don't know who's doing it."
In lower Manhattan, as police, fire and emergency personnel tried to cope with the mayhem, witnesses were in shock.
"I'm sitting down and I'm crying and I couldn't believe that something like this could actually happen," said Tony Bristow, who was working on a nearby pier when the planes smashed in the towers. "Then about 10 minutes later the whole building just started to collapse and now two seconds ago both of them collapsed and now there's no more World Trade Center. It's — this is ridiculous. I don't believe this."
The tops of the twin towers were obscured by the smoke, and thousands of pieces of what appeared to be office paper came drifting over Brooklyn, about 3 miles from the tower.
Before they collapsed, large holes were visible in sides of the landmark twin towers, which were struck by terrorist bombers in February 1993, killing six people and injuring more than 1,000 in attack that at that time shook America.
ABCNEWS' Geraldine Sealey, Dean Schabner, Michael McAuliff, Bryan Robinson, Pierre Thomas, Barbara Starr and Corey Goldman contributed to this report.