Three assailants and a member of Syria's anti-terror squad were killed in a shootout during the bid to storm the embassy.
A fourth attacker who was wounded captured later died of his wounds in hospital before he could be interrogated.
The attack came at a time of particularly tense relations between Washington and Damascus.
Syrian Interior Minister Bassam Abdel Majid told US charge d'affaires
Michael Corbin that the attacker was "providing information to Syrian security authorities," but it was not immediately known who was behind the assault, State Department Spokesman Tom Casey said.
But Syrian authorities later said they were not able to gather information as to who carried out the attack.
Mr Casey said the attackers used two vehicles containing explosives, one of which approached the front of the embassy and the second moved toward the rear of the compound.
"The vehicle near the front of the compound did, in fact, explode, the other wasn't detonated," he said.
The Syrian state news agency SANA quoted Interior Minister General Bassam Abdel Majid as saying "the terrorist attack failed. It did not achieve the objectives of the criminals responsible."
SANA also described the attackers as "takfiri" or Islamic extremists, although no group has yet claimed responsibility.
US praises Syria
The United States praised Syria's action in foiling the attack, while several other nations vowed to boost security at their missions in Damascus and US embassies on their own soil.
"I do think that the Syrians reacted to this attack in a way that helped to secure our people and we very much appreciate that," US Secretary of State Condoleezza Rice said.
"It also once again illustrates the importance of Syria being an important ally in the war on terror," added White House spokesman Tony Snow.
"We are hoping they will become an ally and make the choice of fighting against terrorists."
Relations between Washington and Damascus have been strained over Iraq, the war in Lebanon and Syria's support for Palestinian militants opposed to the peace process with Israel.
Last week the White House branded Syria and its top regional ally Iran "especially worrisome" threats.
"All embassy personnel and their family members are safe," the US embassy said in a statement, adding that the mission would stay closed for at least another day and calling on Americans to adopt a low-profile.
"The Syrian government has pledged full security cooperation."
US policies ‘regrettable’
But the Syrian embassy in Washington said "it is regrettable that US policies in the Middle East have fueled extremism, terrorism and anti-US sentiment.
"The US should take this opportunity to review its policies in the Middle East and start looking at the root causes of terrorism and broker a comprehensive peace in the Middle East."
The attack was the latest in a series against US diplomatic missions across the globe, the most recent being in March 2006 in Pakistan on the eve of a visit by US President George W. Bush.
Although the attackers failed to penetrate the high barbed-wire-topped walls of the compound, one reinforced glass window near an entrance door was pierced by a bullet.
The incident came a day after the fifth anniversary of the September 11 attacks by the Al-Qaeda network of terror mastermind Osama bin Laden and followed a warning by his number two Ayman al-Zawahiri that the Gulf and Israel would be the next targets.