The report by the commission led by Serge Brammertz, a Belgian prosecutor, also reported "considerable progress" in its work but stopped short of setting out new findings on who was behind the crime.
The report also said continued co-operation from Syria "remains crucial".
Brammertz handed over his long-awaited report to Kofi Annan, the UN secretary-general, in New York on Saturday.
The commission, in its fourth progress report to the UN Security Council, also said it supported a request by the Lebanese government that the inquiry be extended for up to another year.
Al-Hariri, was killed by a huge bomb in broad daylight as his motorcade travelled along a Beirut street on February 14, 2005.
Concerning the killing, the commission said the investigation's "fundamental building blocks", including the explosion, the carrier of the explosive device and its means of delivery were "largely understood and provide the basis for investigative progress with regard to those who perpetrated the crime".
Only additional investigation would "lead to the strengthening or exclusion of some of the existing case hypotheses", the report added.
The Brammertz commission is also looking into 14 other bomb attacks in Lebanon to determine whether they were linked to the al-Hariri assassination.
Its report said the cases "can be linked in a number of different ways", but there was as yet insufficient evidence to allow the perpetrators to be identified and linked.
The UN Security Council is set to discuss the report on June 14.
Al-Hariri was killed by a massive
bomb in Beirut last year
Syria, the dominant force in Lebanon since the middle of the 1975-1990 civil war, ended its 29-year military presence in its smaller neighbour 14 months ago after an international outcry over al-Hariri's killing.
Lebanon is working with the UN to set up an international tribunal to try the suspected assassins.
Four Lebanese former security generals have been charged in connection with the crime but no indictments have been issues so far.
In a related development, Nabih Berri, Lebanon's pro-Syrian parliament speaker, on Saturday asked Hosni Mubarak, the Egyptian president, for Arab help in defusing the simmering crisis between Beirut and Damascus.
"The aim of my visit to Cairo is to seek an Arab mediation that would ensure the implementation of decisions" reached during Lebanon's protracted political roundtable talks, Berri said after meeting Mubarak.
At Berri's initiative, Lebanese politicians - Christian and Muslim, pro- and anti-Syrian - have been holding talks since March in a bid to break a political deadlock since al-Hariri's assassination.
Berri said he had received "a very positive response" from Mubarak and informed the Egyptian president of the latest developments in Lebanon's rocky political consultations.