The statement - which Al Jazeera says bears Osama Bin Laden's signature - also urged Muslims to unite against Americans and Jews.
No-one has been able to confirm the authenticity of this or previous Bin Laden messages broadcast by Al Jazeera, a Qatar-based satellite channel. There is also widespread speculation about whether the Saudi-born militant is still alive.
"The heroic operation in Kuwait proves the level of danger that threatens US forces in Islamic countries," the typed statement said.
"The priority in this war at this stage must be against the infidels, the Americans and the Jews who have not stopped their injustice," it went on.
The BBC's Middle East correspondent, Paul Wood, says that while the authenticity of the message cannot be verified, the tone of voice is characteristic.
It is the second statement alleged to be from Bin Laden which the TV station has released in just over a week.
Evidence
Last Tuesday, two gunmen killed one US marine and injured another during military training on the southern island of Failaka.
Kuwaiti security forces have arrested 15 people, who are being held awaiting charges.
The country's interior minister has said an organised group planned to attack other US and foreign targets - but he expressed doubt the attackers had received orders from Osama bin Laden's al-Qaeda network.
On Monday, the US embassy in Kuwait said that in a separate incident, shots had been fired from two civilian vehicles at American troops training in northern Kuwait.
The embassy said the American soldiers had not returned fire and there had been no injuries.
The French tanker, the Limburg, was carrying 400,000 barrels of crude oil when a blast ignited a fire on board on 6 October - killing one crew member and spilling oil into the Gulf of Aden.
On Friday French investigators found traces of TNT explosives on the Limburg, providing the strongest evidence yet that the explosion was due to a terrorist attack.
Yemeni officials initially said the blast was an accident.