Speaking hours after attacks were launched in retaliation for the US embassy bombings which killed 250 people, Mr Clinton said the US was taking a stand against terror organisations who "wrap murder in the cloak of righteousness".
Mr Clinton said that there was "compelling evidence that further attacks were planned by a network of Islamist terrorists."
"Our target was terror, our motive was clear," he said.
'Terrorist' targets
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The two attacks focused on what the US State Department described as a terrorist training base almost 100 miles south of Afghanistan's capital Kabul, and a factory capable of producing chemical weapons in Sudan's capital Khartoum.
US Navy vessels in the Red Sea and the Arabian Sea are believed to have launched Tomahawk cruise missiles.
An Afghan news agency in Pakistan says that the attack there killed 15 people.
In Sudan, reports say that seven were injured in the air strike.
Angry response
Within hours of the attack at 1730GMT (1330EDT) on Thursday, the Taleban authorities in Afghanistan said that the US missiles had missed their target.
The Taleban said it was organising a big anti-US protest in the city of Kandahar.
Two officials from the UN have been shot and wounded in the Afghan capital, Kabul. One of them is said to be in a serious condition.
Shortly after the raid in Khartoum, mass protests began outside the empty US embassy there.
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Sudan said that it would be lodging a complaint with the United Nations over the US air strikes.
The UN Secretary-General Kofi Annan said he was concerned about the attacks, but UK Prime Minister Tony Blair and his Israeli counterpart, Binyamin Netanyahu, supported Mr Clinton.
The US Secretary of State, Madeleine Albright, has asked other nations to support the US stand.
Reaction in the US itself was split between politicians backing the president and those suggesting that the timing might have been related to Mr Clinton's continuing problems in the Monica Lewinsky affair.
Bin Laden blamed
In his address, Mr Clinton named exiled Saudi Arabian dissident Osama bin Laden as the mastermind behind the embassy bombings in Nairobi and Dar es Salaam.
"There is convincing information from our intelligence community that bin Laden's terrorist network was responsible for these (embassy) bombings," Mr Clinton said.
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Mr Clinton also blamed Mr bin Laden's network for the deaths of American, Belgian and Pakistani peacekeepers in Somalia, a plot to assassinate the Pope and the president of Egypt, a bombing of the Egyptian embassy in Pakistan and the murders of German tourists in Egypt.
But, he said, the action should not be interpreted as an attack against Islam: "Our actions were aimed at fanatics and killers who wrap murder in the cloak of righteousness."
Speaking in Washington after the attacks, the US Defence Secretary William Cohen denied that the strikes had been aimed at assassinating Mr bin Laden.
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But speaking to the BBC from Afghanistan, Taleban spokesman Abdul Haye Mutmaeen said that although Mr bin Laden was unharmed, there had been other casualties.
Sudanese Interior Minister, Abdul Rahim, said that the target in Khartoum had been the private Shifa pharmaceutical plant which had nothing to do with chemical weapons.
He added that Sudan had no chemical weapons factories.
Attacks on US 'will continue'
Mr bin Laden, a Saudi millionaire dissident, spoke to the BBC by satellite phone one hour before the attack, denying involvement in the embassy bombings.
However, he said he would continue his war against the Americans and the Jews until the liberation of the Islamic holy places.
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