The Security Council gave the 50-member team led by German prosecutor Detlev Mehlis a renewable three-month mandate to investigate the February assassination. It began work on 25 May.
Many Lebanese accused Syria of being behind the car bomb that killed al-Hariri, a blast that plunged Lebanon into its worst political crisis since the 1975-90 civil war.
Syria denied being involved but, under international pressure, withdrew its troops from the small neighbour it had dominated for nearly 30 years.
Mehlis will present the council with an interim report on Thursday, and expects to need "only an additional few weeks" to complete the probe, UN spokesman Nejib Friji told reporters.
"The conclusions of the investigation will not affect the stability of Lebanon. On the contrary, the investigation will disclose the truth and will hopefully contribute to putting an end to political assassinations and reinstate the rule of law, a prerequisite for stability and normalcy"
UN spokesman Nejib Friji
Friji said the report might contain "broad aspects of the investigation at this advanced stage" but gave no details.
The report "will certainly not state any finding or any conclusion regarding the investigation", a Western diplomatic source said.
The United Nations ordered the investigation after its fact-finding mission led by Irish Deputy Police Commissioner Peter Fitzgerald found an earlier Lebanese inquiry "seriously flawed".
Mehlis has asked to interview Syrian officials as part of the probe, and is waiting for a Syrian government response.
"Mehlis is looking forward to Syrian cooperation in this regard and is quite confident that the Syrian segment of the investigation will be very, very helpful," Friji said.
Al-Hariri's killing was followed by a string of bombings in mainly Christian suburbs of Beirut, the assassination of two prominent anti-Syrian figures and a botched assassination attempt against a minister.
Local media have speculated that Lebanon risks a slide into instability and anarchy if the investigation implicates Syria in al-Hariri's killing, but Friji denied this.
"The conclusions of the investigation will not affect the stability of Lebanon. On the contrary, the investigation will disclose the truth and will hopefully contribute to putting an end to political assassinations and reinstate the rule of law, a prerequisite for stability and normalcy," he said.
Last week, the Finance Ministry announced it was beefing up its foreign exchange reserves to weather any political or economic turbulence that could result from the probe.