"We in Lebanon ... the Hariri family accept the results of the report and the conclusions that the commission sets forth," Saad al-Hariri said in a televised statement from the Saudi city of Jedda on Saturday.
"We call on the international community to uphold its support for the international commission into the assassination of Mr Hariri to unearth the full truth and bring the perpetrators to justice in an international court. We are not seeking revenge, we are seeking justice," he said.
Al-Hariri and 20 others were killed on 14 February by a bomb in Beirut. The UN report said the decision to kill the former prime minister "could not have been taken without the approval of top-ranked Syrian security officials" colluding with counterparts in Lebanon.
Syrian officials dismissed the report as political and said the charges were false.
Al-Hariri's son said he was "very encouraged" by UN Secretary-General Kofi Annan's decision to extend the mandate of the commission so it "can continue its professional work in arriving at the whole truth in the terrorist crime".