Rejecting Lebanon's call for major involvement in the inquiry, the draft given to the 15 Security Council members calls for the international investigating commission to complete its work within six months.
But China's UN ambassador Wang Guangya, the current council president, said there was still a debate over the probe's duration, and diplomats said it could be reduced to three months.
The US-French draft did not include many amendments sought by the Lebanese government, which wanted the investigators to cooperate closely with the government, to be based in Lebanon, and to limit the probe to 12 weeks.
Instead, it would allow UN Secretary-General Kofi Annan to recruit "impartial and experienced staff" without getting agreement from the Lebanese government, and give the commission authority to determine its own procedures.
The draft still says the commission would assist Lebanon in the investigation "of all aspects of this terrorist act", but leaves the commission to decide what role Lebanese authorities would play.
The Americans and French also rejected proposed Lebanese amendments, which would give the investigators the right - not the "authority" - to collect any additional evidence and information, and would let them interview "officials", but not "all officials".
The resolution follows last month's UN report by a fact-finding team which concluded that the Lebanese probe did not meet international standards and called for an entirely new one by an outside team.
Al-Hariri's assassination has
brought massive political change
The team was led by deputy Irish police commissioner Peter Fitzgerald.
The Lebanese wanted the draft to simply note the secretary-general's findings and conclusions based on Fitzgerald's report.
But the French and Americans kept in the report's conclusion that "the Lebanese investigation process suffers from serious flaws and has neither the capacity nor the commitment to reach a satisfactory and credible conclusion".
Point of agreement
The new draft does include one proposal sought by the Lebanese - an endorsement of Annan's opinion "that Lebanon is passing through a difficult and sensitive period, that all concerned should imperatively behave with the utmost restraint and that the future of Lebanon should be decided strictly through peaceful means".
Al-Hariri's 14 February killing caused an uproar in Lebanon, sparking massive anti-Syrian street protests that forced the pro-Syrian Beirut government to resign.
The Lebanese opposition claimed Syria orchestrated the killing and demanded Damascus end its interference in Lebanese politics and withdraw all of its thousands of troops from the country.
Syria denies any involvement, but pledged to withdraw its army and intelligence agents from Lebanon by 30 April during a weekend meeting with UN envoy Terje Roed-Larsen, a move welcomed by Annan.
UN spokesman Fred Eckhard said a UN verification team would be sent to Lebanon "to ensure the full Syrian withdrawal".
Meanwhile, US President George Bush warned Syrian-backed leaders in Lebanon against postponing next month's elections.
President Bush has urged polls in
Lebanon to be held on schedule
"It is important for this election to take place on time," Bush said of the parliamentary poll due in May.
Speaking a day after Syria promised to end its military and intelligence presence in Lebanon by 30 April in line with US and UN demands, Bush said: "I appreciate the fact that Syria has expressed its intent to fully leave the country."
He added: "When they say, 'We're going to leave the
country,' we expect troops and security forces to leave."
In a related development, a south Lebanon local official Umar Zuhairi said the Shebaa Farms were Lebanese, in response to comments by UN envoy Roed-Larsen on Sunday.
Roed-Larsen had said from Damascus that the UN regarded the disputed land as Syrian territory, while Syrian Foreign Minister Faruq al-Sharaa had no comment.
The UN envoy added: "This issue has been behind us for five years now, and it was decided and resolved by the UN Security Council five years ago in a unanimous decision. I have nothing further to comment on."
But Zuhairi said: "Larsen's statement doesn't have any certified basis ... Shebaa Farms are Lebanese because the Israelis didn't occupy it in 1967 as they say, but occupied it in 1985. The owners of the farms still have their deeds to the lands."