Rice on Thursday met Saad al-Hariri, who entered Lebanese politics after the 14 February 2005 killing of his father, in her office and invited in cameras to record the event.
Al-Hariri heads the majority bloc in Lebanon's parliament. The assassination of Rafiq in Beirut set in motion a UN campaign to end Syria's domination of Lebanon.
Syria, under UN pressure, withdrew its troops but its influence has not been entirely erased.
"We will continue to make sure there is no intimidation of the Lebanese people," Rice said, "and that Syria respects its obligations" under UN resolutions calling for it to withdraw its forces from the neighbouring country.
Lebanon can be certain of international support for its independence, Rice said.
Al-Hariri's father, whose relation with Syria witnessed several ups and downs, was killed with 20 other people in a bomb attack as he was driven through the Lebanese capital.
On Friday, the son takes his appeal for US support to George Bush, the US president, at the White House.
Al-Hariri said he hoped UN investigator Serge Brammentz, while new to the post, could do his work quickly and that Syria would co-operate with him.
Jumblatt (R) wants the UN probe
to cover other assassinations
"At the end of the day, knowing the truth is a protection for the whole region," al-Hariri said after he saw Rice.
"The killers of Rafiq al-Hariri must be punished, and if not punish then anybody will start killing others, and this is something we don't want at all to happen in Lebanon," he said.
Meanwhile, Lebanese Druze leader and prominent anti-Syrian figure Walid Jumblat has told the French daily Liberation that an international tribunal must be set up to try the suspected killers of al-Hariri.
Published in the Friday's edition of the paper, the interview quoted Jumblatt as saying that the ongoing investigations should be widened to cover other assassinations in Lebanon.
"All we can do is stick to our basic position: demand an international tribunal and widen the enquiry to include other assassinations," said Jumblatt, speaking from his home in Mukhtara in the Chouf mountains.
The prospect of an international tribunal has led Hizb Allah and Amal movement, two minority Lebanese parties close to Damascus, to boycott the cabinet from 12 December.
"The only thing that can hurt the Syrian regime in the long term is an international tribunal. I repeat, the long term," said Jumblatt.
"The assassinations (in Lebanon) will not stop ... . They are trying to scare us. That is why the Syrians killed Hariri," he said.
Serge Brammertz took up his job
on Monday as the UN probe chief
In other news, on Thursday a senior UN legal expert arrived in Beirut to discuss Lebanese calls for such a tribunal, but the world body has not gone as far as saying such a court would definitely be established.
"My mission is to help the Lebanese government define the nature and scope of required international assistance," Nicolas Michel, the UN undersecretary-general for legal affairs, said.
On Wednesday, Stephane Dujarric, a UN spokesman, said in New York that the mandate of the expert now in Beirut, Nicholas Michel, covered "the killing of former prime minister al- Hariri and others to be tried by a tribunal of an international character".
The visit comes shortly after Serge Brammertz, the new chief of the UN inquiry into the al-Hariri assassination, officially took up his duties on Monday in the Lebanese capital.
His predecessor, Detlev Mehlis, found "converging evidence" of Syrian and Lebanese intelligence officers' involvement in al-Hariri's killing in a blast on the Beirut seafront. It also cast doubt on Syria's co-operation with investigators.