The President said, "On my order, coalition forces have begun targeting selected targets of military importance to undermine Saddam Hussein's ability to wage war."
He added that the strikes were only the beginning of a "broad and concerted campaign" that will involve more than 35 countries aimed at topping the government of Iraqi President Saddam Hussein.
"In this conflict, America faces an enemy who has no regard for the conventions of war or the rules of morality," the president told a television audience.
Mr. Bush said that Iraqi leaders have placed military equipment -- and potential U.S. targets -- in civilian areas, a move he called a "final atrocity." He said that coalition forces will "make every effort to spare innocent civilians from harm."
The president also warned that the conflict in Iraq would be "longer and more difficult than some predict," adding that the effort to create a "united, stable and free country" after Saddam is removed will require a "sustained commitment" on the coalition's part.
To the Iraqi people, the president reiterated that the U.S. has "no ambition in Iraq except to remove a threat and restore control ... to [Iraq's] people," telling Iraqis that "millions of Americans are praying with you," for a quick end to the conflict.
In a formal notice to congressional leaders delivered Wednesday, Mr. Bush said the war in Iraq was a "vital part of the international war on terrorism."
The attack came as dawn was breaking in Iraq and as 300,000 U.S.-led troops were readying for a larger strike.
As the president's address aired on television, American messages were also reportedly being broadcast on Iraqi radio stations, telling listeners, "This is the day you have been waiting for," according to news reports.
Some two hours after President Bush's speech, Saddam addressed his country on Iraqi television.
He urged his people to fight back against the U.S. and its allies, saying "draw your sword? no one will be victorious unless he is a man and a brave man." He assured them that those fighting against Iraq would "lose their patience."
Saddam referred to the American president as "the criminal junior Bush" and accused the United States of committing a "shameful crime" by attacking Baghdad.
The Iraqi leader said the attack was conducted by "criminal Zionists." He ended his speech by saying "long live jihad and long live Palestine."