It accuses Damascus of supporting terrorism and developing weapons of mass destruction.
The vote was almost unanimous and has a strong chance of being passed by the full House next week.
"This legislation will send a message to Damascus and the world that the United States will hold accountable nations that support deadly terrorist groups," Eliot Engel, a Democrat and one of the bill's main sponsors said.
Syria denies links to "terrorist groups", but says it backs legitimate resistance to Israeli occupation. It says Palestinian resistance groups have only media offices on its territory.
But the US is loathe to accept Syria's defence. If passed, the bill would curb US exports to Syria.
In addition, it would call upon the US president to select two sanctions from a menu of six, from downgrading diplomatic relations and reducing business ties with Syria to imposing travel restrictions on Syrian diplomats in US.
A White House spokesman said President George Bush had ended his two years of opposition to the legislation.
"Syria needs to change course, change its behaviour, stop harbouring terrorists," White House spokesman Scott Mcclellan said.
Meanwhile, the Syrian government has distanced itself from remarks made by its ambassador to Spain, concerning retaliation against Israel.
Ambassador Muhsin Bilal had told journalists in Madrid on Wednesday that his country would respond militarily if Israel raided Syrian territory again.
"If Israel continues to attack us, what are we supposed to do? Tell them 'welcome'? Of course we will have to defend ourselves by all means."
But his comments were not received well in Damascus.
An official source said the remarks represented the envoy's "personal understanding" of the country's stance, while the official view - expressed in letters to the United Nations urging that Israel be condemned - was unchanged.
Asked about the envoy's remarks, an Israeli security source said the threat of Syrian retaliation was meant to impress the Arab world.
But Israel, the source said, wanted to avoid any escalation of the conflict and that Syria would never start a war.
Israel launched on Sunday its deepest strike into Syria since the 1973 Arab-Israeli war.
Israeli PM Ariel Sharon will hit
enemies "any time any place"
Tel Aviv said it hit a training camp for Palestinian resistance fighters near Damascus on Sunday. Syria said Israel hit a civilian site.
Possibly more attacks
Israeli Prime Minister, Ariel Sharon, has also raised the possibility of further strikes on Syria, saying Tel Aviv "will hit its enemies in any place and in any way".
Criticism and condemnation poured in from around the world over the bombing.
But Sharon was buoyed by support from US President George Bush, although Bush also said Israel must show caution.
Syrian President Bashar al-Assad accused Israel on Tuesday of trying to drag Syria and the rest of the Middle East into wider conflict, telling the London-based al-Hayat newspaper: "This [Israeli] government is one of war and war is the justification for its existence."