"President Emile Lahud received a letter from UN Secretary-General Kofi Annan on this subject and replied on the basis of cooperation," Barri said on Sunday.
"There are clarifications [that we will be seeking] but on that basis we're going to cooperate, because it's in the interest of the Lebanese state that the truth come out within the framework of respect for its sovereignty."
Barri added: "Unmasking the circumstances of this crime is our number one priority, not only because it is a national duty but also to calm people's spirits and put a stop to the false accusations being bandied about."
Earlier, politicians meeting Barri in southern Lebanon had called for an inclusive political discussion following the assassination of former Lebanese prime minister Rafiq al-Hariri.
But, according to Aljazeera's correspondent in Beirut, Ghassan bin Jiddo, the government's call was rejected by the opposition on Sunday.
Al-Hariri was killed last week in
a massive explosion in Beirut
Pro-government parties along with Syria allies are to hold an extended meeting in Ain al-Tina area in Beirut to discuss the opposition's rejection of their calls for unconditional talks between the factions, bin Jiddo said.
On their part, opposition activists started preparations on Saturday night near al-Hariri's grave, preparing for rousing speeches and anti-government and anti-Syrian slogans.
They have also started to set up tents near al-Shuhada statue in central Beirut square.
The government will not remain silent on this issue, bin Jiddo said, adding that the situation could lead to security disturbances and even violence.
Aljazeera has learned that Lebanese security forces might bring pressure to bear on the opposition to disband its plans.
Earlier, Lebanese journalist Cilina Nasser told Aljazeera.net the political atmosphere in Beirut was palpable.
As of now the confrontation is limited to the level of rhetoric, the opposition having called on Friday for a "peaceful intifada".
But opposition members are living in fear for their lives, especially Druze leader Walid Jumblatt who thinks he is "next on the list", Nasser added.