President Clinton was woken at 5.30 in the morning to be informed of the bombings of the US embassies in Kenya and Tanzania. No advance warnings were reported.
He later said: "These acts of terrorist violence are abhorrent. They are inhuman." He ordered flags on all government buildings at home and abroad to be flown at half-mast.
The President also ordered medical teams to be rushed to Nairobi and Dar es Saalem by military air transport. A 40-strong Marine Corps anti-terrorist team was also ordered to the African countries and FBI specialists were also mobilised.
The Secretary of State, Ms Madeleine Albright, who was in Rome for the wedding of the department spokesman, Mr Jamie Rubin, to the CNN correspondent, Ms Christiane Amanpour, also condemned the bombings.
She later flew back to Washington.
US officials warned against hasty conclusions about who might be responsible for the attacks. A White House spokesman would not comment on a report that the Islamic Jihad terrorist group has recently threatened to retaliate against the United States for the extradition of three of its members from Eastern Europe. But he said that the US authorities had "some ideas" on who might be responsible for the bombings based on intelligence sources.
President Clinton was briefed at regular intervals throughout the day on the bombings. He also spoke to the ambassador in Nairobi, Ms Prudence Bushnell, who was slightly injured in the blast.
The newly appointed ambassador to Tanzania, Mr Charles Stith, was out of the country on holiday. He called the bombing "brutal, heinous and cowardly".
The White House spokesman said that the President hoped to speak to the Presidents of Kenya and Tanzania. He would thank them for the cooperation of their people in rescuing victims from the blasts and offer condolences for the deaths of the numerous Kenyans and Tanzanians who had been killed and injured although it was clear that the US embassies were the target.
In a statement he read at a ceremony at the White House, President Clinton said that although the attacks appeared to be co-ordinated, no one had claimed responsibility. Security measures at US embassies and military facilities in the region and around the world had been stepped up.
Mr Clinton promised to "use all means at our disposal to bring those responsible to justice no matter what or how long it takes". He said: "We are determined to get answers and justice."
The Speaker of the House of Representatives, Mr Newt Gingrich, who is about to travel to Ireland, called for improved intelligence to capture the terrorists. "We should do everything we can to track down the people who have done this and to make them pay to the fullest extent," he said.