Iraq fired a total of six missiles on northern Kuwait, two of which were intercepted by Patriot missiles, Kuwait's defence ministry says.
Air raid sirens wailed repeatedly during the morning in the emirate amid fears of chemical attack as Baghdad hit back against US forces.
The first two missiles crashed into the Mutlaa desert of northern Kuwait around 7.30 a.m. Irish time. Some two hours later, the ministry announced that three more missiles had hit Kuwait. The sirens sounded again and the ministry said a sixth missile had arrived.
Several countries denounce the start of the conflict. Protests also begin in several capitals.
"China calls for a prompt halt to the military action against Iraq so as to avoid casualties of innocent people," said the Chinese foreign minister.
"As the first military operation in Iraq starts, the French authorities express their deep concern," the French Foreign Ministry said in a brief statement. Russia's President Putin said: "This military action is unjustified ... there has been no answer to the main question which is: are there weapons of mass destruction in Iraq and, if so, which ones."
Iraqi officials say at least one person is killed after air strikes on Baghdad.
Nine people were in a serious but stable condition with shrapnel injuries at Baghdad's Al-Yarmouk Hospital, Dr Jamal Abed Hassan said.
They included six members of one family that was having breakfast when their town 20 miles west of Baghdad was attacked, the doctor said.
The International Committee of the Red Cross (ICRC) later confirms one person died and 14 were injured in the opening raid.