Hezbollah chief Hassan Nasrallah last week displayed what he said was Israeli surveillance footage of routes used by Hariri, saying this pointed to Israel carrying out the suicide bombing which killed the former prime minister and 22 others.
Nasrallah displayed the footage a few weeks after he was told the Special Tribunal for Lebanon may indict some of the group's members over the Hariri killing, an allegation he categorically rejects.
He has strongly criticised the UN tribunal and attacked it as an "Israeli project", raising fears of renewed potential conflict between the Iranian-backed militant group and the US- and Saudi-backed Prime Minister Saad al-Hariri, Rafik's son.
At a gathering late on Monday Hariri called for calm, saying Lebanon should not fear "any political noise, which we hope to calm down and turn into calm speech, and start democratic dialogue".
On Saturday, he said he wanted to know who killed his father but at the same time he wanted stability. "Dialogue cannot succeed with the accusations of treason and with repeated calls for tests of patriotism and nationalism," Hariri said.
After Nasrallah's two-hour presentation of footage, witness testimonies and analysis aimed at making a case that Israel was behind the assassination, the Office of the Prosecutor at the UN tribunal asked Lebanese authorities to provide all information in Nasrallah's possession, including the footage.
Lebanese Prosecutor Saeed Mirza passed on the evidence, which he received from senior Hezbollah official Wafiq Safa, to the chief prosecutor Daniel Bellemare's office in Lebanon, judicial sources said.
Hariri formed a national unity government last year which includes Hezbollah ministers. Analysts say if the tribunal does indict Hezbollah members, the group, together with Shi'ite and Christian allies, could decide to collapse the government.
As-Safir newspaper said on Tuesday Hariri and Nasrallah's assistant Hussein Khalil held a late night meeting on Sunday. It quoted sources describing the meeting as "positive and very useful".
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