"Unknown assailants fired on Sunday at 2:25 am (2325 GMT Saturday) three rockets from an assault rifle, and not RPG rockets as initially reported, towards a building near UN House," a police officer told AFP.
"Six civilians were slightly wounded by one of the rockets which exploded against a building next to the UN offices," the officer added, asking not to be named.
Police said one rocket smashed through a window of the building and injured people inside, a second exploded against a wall leaving a black impact while a third exploded on the sidewalk, damaging two cars.
The building hit by the rockets houses the offices of several companies, two restaurants and the headquarters of the charity foundation of Saudi billionaire Al-Walid bin Talal.
It was the third security breach in Beirut in the last 10 days, following two hand-grenade attacks which earlier targeted police stations without causing casualties.
Sunday's attack was the first to target the downtown area where tight security has been in place since the February 2005 massive car bombing that killed popular prime minister Rafiq Hariri.
The area houses the sand-bagged UN House, the prime minister's offices and foreign diplomatic missions.
"The UN House was not hit. We don't believe that the UN House was the target of this regretful incident," a UN official told AFP on condition of anonymity.
Lebanese soldiers cordoned off the area and were seen picking up shrapnel. One soldier told AFP that the assailants probably fired on the building from a nearby parking lot, close to UN House.
Lebanese Interior Minister Ahmed Fatfat told LBCI television on Sunday that "this the first time that civilian buildings (have been) hit in central Beirut."
"It is a clear attempt to breach security," he said, without elaborating.

Copyright AFP (Agence France-Presse), 2006