The president considers the government of the prime minister, Fuad Siniora, to be unconstitutional since six cabinet ministers resigned last month shortly before the government initially approved the tribunal.
Lahoud also sent a message to Kofi Annan, the UN secretary-general, informing him of his refusal to ratify the document.
Al-Hariri's killling plunged Lebanon into
"Once a constitutional government is put in place, I will take action in order to correct the constitutional mistake," the statement said.
A presidential spokesman had already rejected the cabinet's vote the day after the meeting.
Lahoud's endorsement is not necessary for final approval of the tribunal.
However, the next step does require the approval of parliament speaker Nabih Berri, a prominent Shia leader of the Amal movement which also regards the current government as illegitimate.
Berri said last week he would not convene parliament until the government's current crisis is resolved.
An ongoing UN probe has implicated senior officials from Syria, which for decades was the powerbroker in its smaller neighbour, and their Lebanese accomplices.
Damascus strongly denies any connection with the al-Hariri killing.
Lebanon has been in political turmoil since al-Hariri's murder in February 2005, and the deadlock has escalated this month with an open-ended sit-in by thousands of opposition demonstrators outside Siniora's offices.
The opposition, led by the Shia group Hezbollah, wants a new, national unity government, no longer recognises the current cabinet after the six pro-Damascus ministers resigned.
Fresh protests are planned for Sunday in the capital and the opposition has warned it may block airports, ports and main roads beginning on Monday in a bid to force its demands.