The official Syrian Arab News Agency said on Saturday that President Bashar al-Asad's talks with a US Homeland Security Committee delegation, led by California Republican Christopher Cox dealt with combating "terrorism" and the Arab-Israeli peace process.
It said the talks tackled "the necessity for establishing a clear, constructive and reasonable dialogue".
Washington wants Syria to crackdown on Lebanese and Palestinian resistance groups, halt the alleged development of unconventional weapons and withdraw its 20,000-strong military presence from Lebanon.
The bill also authorises Bush to bar trade in dual-use items that could be used in weapons programmes and demands Damascus secure its border with Iraq. Washington accuses Damascus of allowing fighters to infiltrate Iraq from Syria, a claim Syria denies.
Cox told a news conference, after what he said was a very constructive meeting he was encouraged "that there is a prospect for getting Syrian-US relations back on track".
But he added: "I can't say that I sensed that there was a diplomatic breakthrough today... I can report back from those discussions that the president fully appreciates - which is a different word than agrees with - the American position."
The Syrian leader said that the legislation could be viewed as a "glass half full" since the bill included expanding relations with Damascus if the sticking points could be resolved.
Earlier, Syrian officials said the US law lacked justification.
Cox says there are prospects for
improving US-Syrian ties
Oil Minister Ibrahim Haddad said if US companies were to withdraw from Syria it would be business as usual. But he admitted the move could block new US investment.
Implementing the law would only increase tensions instead of searching for common factors to achieve stability, reported the state-run radio.
The US stance contrasts with that of the European Union, which announced a breakthrough in talks to agree a political and economic cooperation pact earlier this week.
An EU official said the pact allowed for dialogue with Syria on "terrorism", weapons of mass destruction and human rights.
Syria's spokeswoman for the foreign ministry, Buthaina Shaaban, speaking before Bush signed the legislation, said that there was no justification for the US bill.
She said that the law was passed because of Syria's opposition to Israeli occupation of Arab land and its support for the Palestinian uprising. Israel occupied the strategic Syrian Golan Heights in 1967 and annexed the area in 1981.