The move by the US president reinforced suspicions about Syrian involvement in the Beirut truck bombing that killed al-Hariri and 20 others on 14 February, 2005.
In an executive order, Bush authorised the secretary of the treasury to freeze assets of people who are determined to have been involved in al-Hariri's death or to have obstructed the work of UN investigators.
A UN commission has linked Syrian and Lebanese intelligence agents to al-Hariri's death. Bashar al-Assad, the Syrian president, has denied the accusations.
The order also targets anyone involved in an assassination or bombing in Lebanon since October 1, 2004, related to al-Hariri's killing or implicating the Syrian government, an administration official said.
Separately, the US ambassador to the UN, John Bolton, said on Wednesday that the US wants a new Security Council resolution on what it calls continued Syrian interference in Lebanon and Iran's backing of guerrillas there.
Bolton said the council should react to a recent report from Kofi Annan, the UN chief, which urged a delineation of borders between the two countries.
It also called for disarming Iranian and Syrian-backed Hizbollah fighters in the south, and establishing formal diplomatic ties.
Bolton wants Syrian 'areas of
The report, prepared by the UN envoy Terje Roed-Larsen, is a response to Security Council resolution 1559 of September 2004 that called for Syria to withdraw from Lebanon and for Beirut to disarm militia so it could control the entire country.
"We think a resolution would be appropriate at this point," Bolton said. "I think highlighting the areas of deficiency in Syria's performance ... would be important to show the Council's continuing resolve."
But China's UN ambassador, Wang Guangya, this month's council president, was cautious.
"The region is already complicated, we don't want to make it more complicated. We are not so enthusiastic about more resolutions," Wang said.
And Syria, in a letter, said Annan's report exceeded the mandate of the September 2004 resolution. Setting borders and establishing diplomatic relations fell "within the domestic jurisdiction in both countries".
Bolton also said the resolution could include a call for Syrian co-operation with the investigation into the murder of al-Hariri
For its part, Lebanon plans to ask the UN to extend the inquiry, according to the information minister, Ghazi Aridi.
"We will ask for a one-year extension maximum and it will be up to the UN Security Council to decide," Aridi said after a weekly cabinet session on Wednesday.