President Bush has confirmed that US-led forces have launched a military strike against Iraq.
"On my orders, coalition forces have begun striking selected targets of military importance to undermine Saddam Hussein's ability to wage war," Bush said.
Bush said the military operations were the "opening stages of what will be a broad and concerted campaign".
Saddam condemned the attack and vowed to defend Iraq.
The declaration of war came just hours after an ultimatum expired for the Iraqi leader to give up power.
News agencies reported missile strikes against targets in Baghdad during the early hours of Thursday morning (local time).
The head of the international Red Cross called on all sides in the war to abide by the Geneva conventions, and spare civilians and prisoners.
"Even in wars people have rights that must be protected," said Jakob Kellenberger, president of the International Committee of the Red Cross.
As dawn broke over the Iraqi capital, heavy explosions were heard in the city and on its southern outskirts. Jets were reported flying overhead, while anti-aircraft batteries opened fire.
The White House said the attack was aimed at "very senior" Iraqi leadership.
"I assure you, this will not be a campaign of half measures and we will accept no outcome but victory," Bush said.
In the first hours, at least 40 cruise missiles were launched against Baghdad from the US positions in and around the Gulf.
US officials said the attack before dawn was limited and not the beginning of a larger campaign expected in the coming days and hours.
Test of patience
Saddam appeared on state television to urge Iraqis to defend their country, vowing to push US-led forces to their "limit".
"In the name of the Iraqi people, we will promise our Arab nations and friends that we will fight our occupiers until they lose their patience," Saddam said.
He also condemned the US and Britain for "shameful crimes against Iraq and humanity" following the attack.
Saddam finished his speech, saying "long live Jihad [holy war]and Iraq, defeat to invaders".
Call for resistance
A radio station controlled by Uday, Saddam's son, issued a statement calling on people to resist.
"This is our day. Let us start the fight. We will be victorious. We will die as faithful martyrs," the station was reported saying.
The US said the war was necessary because Iraq had refused to give up its alleged stockpiles of chemical and biological weapons.
It also follows the collapse of diplomatic attempts to avert a conflict.
Bush said American and coalition forces were in the early stages of an operation to free the Iraqi people.
"Now that conflict has come, the only way to limit its duration is to apply decisive force," Bush said.
News agencies reported that US infantry units had moved closer to the Iraq-Kuwait border, in preparation for an expected ground invasion.
The US has deployed around 235,000 military personnel in the Gulf region and Britain has committed some 45,000 troops.
Australia has also deployed around 2,000 troops. Around 20 countries have provided logistical support, ranging from troops to access to airspace.
Iraq is believed to have some 350,000 troops, an air force and small navy.
Colonel Chris Vernon, a British military spokesman, said US and British forces have not yet received orders to launch a ground attack.
The US army said it had launched a fresh military operation in southern Afghanistan on Thursday morning (local time) with an air assault southeast of the city of Kandahar.
Bush earlier told Congress that American forces had launched a raid in Afghanistan at the same time as operations in Iraq.
News agencies said about 1,000 members of the 82nd Airborne Division had moved into villages in Afghanistan's southeast, searching for al-Qaida members.
Breaking story, more to follow.
swissinfo with agencies
Bush has announced the start of military operations against Iraq.
Heavy explosions have been heard in Baghdad and on the city's southern outskirts.
Jets have been reported flying over the city. At least 40 cruise missiles have been fired.
US military officials say the pre-dawn attack on Baghdad is a precursor to a larger campaign.
Bush says war "will not be a campaign of half measures".
Saddam has vowed to "fight our occupiers until they loose their patience".
US-led troops are reported to be gathering at the Kuwait-Iraq border.
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