The official Syrian Arab News Agency said on Wednesday: "The fourth terrorist died from severe wounds. He could not be interrogated. All four carried Syrian nationality."
Syrian security forces killed three of the four men who made a botched attempt to blow up the embassy. A Syrian guard was also killed and 13 people were wounded. No Americans were hurt.
No group has claimed responsibility for the attack, which officials privately blame on Islamist militants.
Friends or allies
The US thanked Damascus for its swift response to the embassy attack and said it hoped Syria "will become an ally" in the fight against terrorism.
Syria's ambassador in Washington, Imad Mostafa, said his government was ready for dialogue, but urged the US to change policies that has fuelled resentment in the Middle East.
"US policies have created a lot of hostility in the region and this is the time to re-evaluate them. The ball is in the American court," he told al-Thawra newspaper.
Syria is listed by the US as a sponsor of terrorism due to its support for Lebanon's Hezbollah movement and armed Palestinian groups.