Syrian representatives said that the government had not been consulted on the plan, according to the letter which was addressed to Kofi Annan, the UN secretary-general.
Annan was authorised by the Security Council last Tuesday to ratify a UN-Lebanese agreement to create the tribunal.
On November 13, the Lebanese council of ministers approved the tribunal plan, but Emile Lahoud, the pro-Syrian president, challenged the decision. He says that due to the resignation of a number of Hezbollah ministers, the decision was unconstitutional.
"Due to the resignation of a number of Hezbollah ministers, the decision was unconstitutional".
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Fouad Siniora, the Lebanese prime minister, has called for a cabinet session on Saturday to approve the proposed court. The government is now expected to make the final decision on the establishment of the tribunal.
It would sit outside Lebanon, and a majority of judges as well as the prosecutor would be from other nations.
On Wednesday, the Security Council approved a request from Lebanon for UN investigators already looking into the al-Hariri assassination to assist in the investigation of the killing of Pierre Gemayal, who was shot dead in Beirut on Tuesday.
An ongoing UN investigation into the February 2005 truck bombing that killed al-Hariri and 22 others has said the complexity of the attack suggested the Syrian and Lebanese intelligence services played a role.
Syria announced that the hasty adoption of the court's statute "will firmly establish our belief that Syria has no connection with this tribunal".
"In the event that the statute of the tribunal is adopted, unacceptable transgressions that undermine the sovereignty of certain member states and the rights of their subjects are likely to transpire," Syria wrote.
The Syrian government continues to co-operate in the investigation, the letter added.