"It's an accurate statement that we have concerns about ties to al-Qaeda," White House spokesman Ari Fleischer told reporters.
The marine casualties occurred when two gunmen fired on them from a pick-up truck on the small island of Failaka off the coast of Kuwait while they were on a training exercise.
According to the BBC Pentagon correspondent, Nick Childs, the US believes the attack was planned locally in Kuwait.
The two gunmen, named as Anas Ahmad Ibrahim al-Kandari, 21, and Jassem Hamad Mubarak al-Hajeri, 26, were killed by other marines shortly afterwards.
A spokesman for the US Navy Fifth Fleet based in Bahrain said the injured marine was recovering.
His dead comrade was identified as Lance-Corporal Antonio Sledd.
A further incident was reported on Wednesday, when US military personnel fired on a civilian vehicle north of the US base at Camp Doha in Kuwait, after apparently coming under threat from it.
The car was forced off the road, but the American vehicle did not stop.
Al-Qaeda link?
The Kuwaiti authorities have arrested some 50 people in connection with Tuesday's attack, many of them relatives or friends of the dead gunmen.
Among those held are four people described as co-conspirators.
A Muslim cleric who said he was a friend of the attackers told the Associated Press news agency that the two attackers had spent six months in Afghanistan.
The BBC security correspondent, Frank Gardner, says that this does not bear the hallmarks of a classic al-Qaeda operation.
Only three Kalashnikov rifles were reported to have been used, he says.
In his view, the most likely explanation is that the gunmen were two individuals who felt so angered by US policy towards Israel and the Palestinians that they decided to strike a blow for their beliefs.
Joint exercise
The Eager Mace exercise, a joint project between the US and Kuwait, began on 24 September amid reports that US forces were preparing for possible military action against Iraq.
But the Kuwaiti Minister for Foreign Affairs, Sheikh Mohammad, said the American troops were in Kuwait for one reason alone: "To protect Kuwait's security and to participate (in exercises) with Kuwaiti armed forces.
"We consider this an attack against Kuwait's national interests," the minister said.
There are already close to 10,000 fully equipped US troops in the country - as many as 1,000 of whom are taking part in the Eager Mace exercises.
Kuwait is the strongest regional supporter of US plans to topple Iraqi leader Saddam Hussein, but many Kuwaitis are nervous about a possible attack.