"He knows how to do that... he has influence, he has regional and international ties and knows the 'cogs' within the Special Tribunal for Lebanon. He can make the necessary efforts to ensure any accusation is not unjust," he said.
Qassem was speaking a day after Hariri, whose ex-premier father was killed by a massive car bomb in Beirut in 2005, ruled out any compromise on the tribunal and Hezbollah vowed to try to block financing for the court.
"We say to Prime Minister Hariri that he follow the necessary contacts so that the truth becomes known... he can tell Saudi Arabia to intervene," Qassem said.
Tensions over the tribunal have grown steadily in recent weeks, raising fears of sectarian violence and the collapse of the national unity government in which Hezbollah has two ministers.
Syria, which supports Hezbollah, and Saudi Arabia, which backs Hariri, stepped in last week in a bid to calm tensions.
A communique issued by the premier's Future Movement said on Wednesday: "It is out of the question to forget the blood spilled by the martyr Rafiq Hariri. We reject any compromise or attempt to do away with the tribunal."
It added that Hariri was keen on seeing the tribunal conclude its investigation into his father's murder, though he did not want that to plunge Lebanon into crisis.
Hezbollah said in July that it expected the UN tribunal, set up in 2007 and based in The Hague, to accuse it of involvement in the Hariri assassination.
Hezbollah and its allies have accused the tribunal of being part of an Israeli plot and of basing its investigation on testimony by "false witnesses".
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