Six ministers resigned in November over the decision to create the tribunal and opposition parties have been holding street protests against the government since December 1.
Nabih Berri, the parliamentary speaker, has refused to reconvene parliament until the political crisis is resolved.
Nicolas Michel, UN chief legal counsel, signed the formal agreement on Tuesday, which was also signed by an official in Lebanon's justice ministry.
"It is up to the competent Lebanese authorities to take the steps necessary under the Lebanese constitution for the approval and ratification of the agreement, to allow it to enter into force," a UN statement said.
"The tribunal could then be made operational with the full support of the United Nations."
Impasse
The UN is hoping that Arab diplomats, who are attempting to defuse the crisis, can find a solution to the impasse over the international court.
"We want the tribunal, but we don't it to be a tool to be used by the authorities against their rivals"
Hassan Fadlallah, Hezbollah MP |
A senior UN official told the Reuters news agency that the world body was willing to explain the impartiality and scope of the tribunal to its opponents if that would help resolve the situation.
The opposition has not given an official reaction to the signing of the accord, but on Wednesday a Hezbollah MP set out the party's problems with the tribunal.
"We want the tribunal, but we don't want it to be a tool to be used by the authorities against their rivals," Hassan Fadlallah said.
"And who tells us that the Americans will not be using the tribunal for their own political interests?"
President's opposition
Lahoud's opposition to the tribunal is well documented and he has accused Fuad Siniora, the prime minister, of violating the constitution when he sent a letter to the UN secretary-general backing its creation.
Siniora's letters included one with a petition from 70 out of 108 parliamentarians approving the tribunal.
Lahoud said the contents of Siniora's letters were "misleading and sidestepped reality and the rules of the constitution, conventions and national unity," according to a copy of a letter he sent to Ban Ki-Moon.
"The purpose of [Siniora's message] is to generate confusion and suspicion and to create an atmosphere for the Security Council to take over the subject and establish the tribunal," he said.
Al-Hariri was killed, along with 22 other people, by a car bomb in Beirut on February 14, 2005. A United Nations commission has been investigating the assassination.