Islamist gunmen launched a brazen assault on the embassy on Tuesday using grenades, automatic weapons and an explosives-laden van, but failed to breach the compound's defences.
Three of the assailants and a member of Syria's anti-terror squad were killed in a shootout during the attack and one of the attackers was wounded and captured.
He later died of his wounds in hospital before Syrian security officers could interrogate him.
The Syrian state news agency SANA described the attackers as "takfiri", or Islamic extremists, although no group has yet claimed responsibility.
"The terrorist attack failed. It did not achieve the objectives of the criminals responsible," SANA reported Syria’s Interior Minister General Bassam Abdel Majid as saying.
"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.
Fourteen people were also wounded in the incident, including an embassy guard and passers-by.
Chinese state media said a Chinese diplomat standing on top of Beijing's embassy nearby had been slightly injured by a stray bullet.
'Fuelling extremism'
The attack came a day after the fifth anniversary of the September 11 attacks in America and at a time of particularly tense relations between Washington and Damascus.
While Damascus condemned the “heinous” attack, the Syrian embassy in Washington was critical of US foreign policy.
"It is regrettable that US policies in the Middle East have fuelled extremism, terrorism and anti-US sentiment,” a statement from the said.
"What has happened recently in Lebanon, the Palestinian territories and Iraq is exacerbating the fight against global terrorism.
"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 statement opened by noting that the US embassy in Damascus was the target of a "heinous terrorist attack by an extremist group."
"In accordance with the Geneva Convention, Syria performed its duties in the best possible manner to protect the US Embassy," the statement said.
"Syrian security forces took the full brunt of the attack, sadly losing one security official while several others were injured."
Earlier Secretary of State Condoleezza Rice praised the Syrian response to the attack.
"We appreciate the response of the Syrian security forces to help secure our territory," Ms Rice told reporters.
The White House, however, took the opportunity to call on Syria to become an ally in the "war on terror."
"It also once again illustrates the importance of Syria being an important ally in the war on terror," said White House spokesman Tony Snow. "We are hoping they will become an ally and make the choice of fighting against terrorists."
Washington's relations with Damascus have deteriorated with the US administration accusing Syria of backing the Lebanese Shiite Hezbollah militia and of failing to prevent foreign fighters crossing into neighbouring Iraq.
Attacker cooperating
US officials said the gunman captured during the attack had been cooperating with Syrian authorities.
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.
He also 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.
A US official speaking on condition of anonymity said the attack apparently went awry when some of the assailants' explosives malfunctioned.