"Names of individuals will only appear in future indictments filed by the prosecutor, where there is sufficient evidence to do so," the report said.
The 10-page report, the 10th to be issued by the UN commission, is the first since Bellemare took over the panel from Serge Brammertz, a Belgian investigator, at the beginning of this year.
Some Lebanese politicians say Syria was behind the bombing but Damascus has denied involvement and the latest UN report identifies no suspects.
An earlier UN investigator, Detlev Mehlis, Brammertz' German predecessor, had implicated senior Syrian officials in al-Hariri's assassination.
For three decades before the killing, Syria maintained troops and political sway in Lebanon.
Bellemare's panel said it had evidence the "Hariri network" existed before the killing, conducted surveillance of its victim and continued, at least in part, to operate after the assassination.
The report said the UN panel was now gathering more information about the network, the identity of all its participants, their links with others and their role in other attacks in Lebanon.
It was also pursuing efforts to identify the suicide bomber, comparing information already obtained with exit-entry records and missing-person files of various countries, as well as conducting DNA profiling.
Last year the UN Security Council set up a special tribunal to try suspects in the al-Hariri killing once the investigation is complete.
Bellemare's report gave no indication of when that would be and warned against expecting indictments soon, saying: "Investigations of this complexity cannot be rushed."
Lebanon's government welcomed the UN report.
"The report is very positive and it is clear that there has been an important advance in the probe," Ahmad Fatfat, youth and sports minister, said.
The investigating commission's mandate expires on June 15 but can be extended.
Besides al-Hariri's killing, the UN panel is also involved in 20 other inquiries in Lebanon, including two murders since its last report.
Bellemare said the lack of extra resources to meet the increased workload had put more pressure on the commission.
UN officials said on Thursday there was now enough money in hand or pledged by donor countries - over $60m - to cover first-year costs of the planned tribunal.
The court will sit in the Netherlands and Bellmere will become the court's chief prosecutor when it begins work.