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 the Hezbollah, which has denied any involvement in Hariri's killing, and allies of the prime minister.
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 vital 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.
Hariri's visit follows a trip to Lebanon last month by Iranian President Mahmoud Ahmadinejad, who stressed support for all Lebanese but also made a high profile tour of Hezbollah strongholds, which highlighted the influence of Tehran's ally.
Tensions over the investigation have already paralyzed Hariri's unity government, which includes Hezbollah ministers.
Hezbollah leader Sayyed 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."
A 2008 political crisis led to street fighting between Hezbollah and supporters of Hariri and analysts warn that indictments against Hezbollah could spark worse violence.
A joint visit to Beirut in July by Saudi Arabia's King Abdullah and Syrian President Bashar Assad helped ease the discord, without reaching solution on avoiding future conflict.
"The framework of the Saudi-Syrian initiative is in place and its road map is there. Now the discussion is in its details," said Okab Sakr, a parliamentarian close to Hariri, adding the initiative will "ensure both justice and stability."
Sakr gave no details of the initiative, which is being kept confidential until it was finalized, but said Iran was satisfied with it. "If Iran objects it, then it will stop but actually there is an Iranian content."
Saad Hariri has maintained support for the tribunal, leading to a standoff with Hezbollah which has left Lebanon with a weakened government unable to push through economic reforms. The country's 2010 budget has been stuck in Parliament since June with no sign it will pass this year.
Lebanese officials said that they were optimistic that the Saudi-Syrian initiative would find the solution but it was on pause until Saudi King Abdullah returns from medical treatment.
