Western diplomats have said that the tribunal could indict members of Hezbollah, which is backed by Iran and Syria, by early next year for the 2005 bombing which killed former Premier Rafik Hariri and 21 others.
Lebanese politicians fear the indictments could prompt confrontation and possible violence between Hezbollah, which has denied any involvement in Hariri's killing, and allies of the prime minister.
Hariri was welcomed to Iran by first Vice President Mohammad Reza Rahimi who vowed to deepen ties with Lebanon. "We should use all of our capacities to expand the ties ... and to take giant steps in line with our interests," Rahimi said after a meeting with Hariri.
Hariri was expected to meet senior Iranian officials, including Supreme Leader Ayatollah Ali Khamenei and President Mahmoud Ahmadinejad during the three-day visit, Iranian television said.
Ahead of his first official visit to Iran, Hariri told Iran's state news agency that Iran could play an important role in allaying tension in Lebanon.
"Iran plays an important role in the Middle East region ... particularly in resolving crisis and maintaining stability in Lebanon," IRNA quoted Hariri as saying.
Ahmadinejad visited Lebanon in October, when he said Iran supported all Lebanese but highlighted the influence of Hezbollah by visiting its strongholds.
Lebanese officials hope a recent initiative by the leaders of Saudi Arabia and Syria will help prevent any escalation. Iran's endorsement of the Saudi-Syrian efforts is essential for their success.
"Hariri's visit ... is a piece in the regional movement toward (accomplishing) the deal," Lebanese analyst Oussam Safa said, adding it will give Hariri direct access to Iran without having to go through Tehran's allies — Hezbollah or Syria.
"It will help Hariri to get Iran's support in calming Hezbollah's reaction if the indictment is issued," he said.
Hezbollah leader Hassan Nasrallah has urged all Lebanese to boycott the tribunal and vowed to block the arrest of any of his members. He has also called on Hariri to repudiate the tribunal, which he described as an "Israeli project".
Iran's English language Press TV quoted Ghazanfar Roknabadi, Iran's ambassador to Beirut, as saying that Hariri's visit was "historically significant" and would have positive results on Lebanon in the next few days, .
"Iran backs unity among Lebanese political groups ... the visit will also be appreciated in Lebanon," said Roknabadi.
Some Iranian papers said Hariri's visit could build a strong front against Israel, which Tehran refuses to recognize. Israel has not ruled out the possibility of a military attack if diplomacy fails to resolve Iran's nuclear standoff.
"The visit will expand ties between Iran and Lebanon and will surely strengthen the resistance movement against the Zionist regime (Israel)," said Deputy Foreign Minister Reza Sheibani, the state-run Iran Daily newspaper reported.