Annan said on Wednesday he expected to release a report in the next few days on a fact-finding mission into al-Hariri's 14 February death in a massive car bomb.
"I believe a more comprehensive investigation may also be necessary. The vicious assassination ... was a severe blow," he said at an Arab League summit in Algiers.
"He was a Lebanese patriot, a formidable statesman and a vital presence in the international community," the UN chief added.
A Lebanese newspaper that al-Hariri owned said on Tuesday the UN report into his assassination was expected to accuse Lebanese authorities of negligence and evidence tampering.
Leaks about the purported contents of the confidential report have emerged in recent days.
Al-Hariri was killed in a massive explosion in central Beirut that ripped through his motorcade and killed 17 others. A UN team dispatched to look into the attack completed its mission in Beirut on 16 March.
"[Hariri] was a patriot, a formidable statesman and a vital presence in the international
In the three weeks of investigating, deputy police commissioner Peter Fitzgerald of Ireland inspected the bomb site and met Lebanese politicians, senior security and judicial officials, as well as members of the opposition.
Al-Hariri's Al-Mustaqbal newspaper quoted various unnamed sources as saying the UN team noted "a clear flaw in the scene of the crime where there was abnormal chaos and lack of coordination among security apparatuses".
It pointed to the discovery of three bodies days after the explosion as evidence of the confusion that surrounded the clean-up operation.
The paper also claimed the fact-finding team found Lebanese security authorities had "tampered with evidence by rushing to tow away al-Hariri's motorcade from the scene of the crime" to a police barracks, "then sending on the same night a bulldozer to fill the [explosion's] crater and cleaning the road in order to open it to traffic".
The Lebanese government has said it is holding its own investigation into the explosion and has not made any official statements.