The request, faxed to The Associated Press on Wednesday, followed Saniora's failure to win the opposition's support for the tribunal.
In the letter, Saniora cited "unjustified difficulties" that hamper the process of ratifying the tribunal in Lebanon and accused pro-Syrian Parliament Speaker Nabih Berri of "paralyzing" the assembly because he refused to convene a session to ratify the tribunal.
"This is why we ask you ... to present this matter to members of the Security Council to study alternative means and ways that will lead, without any delay, to the creation of the tribunal," Saniora wrote. "We are convinced that justice, peace and security in our country and region is at stake."
Saniora's letter was sent to U.N. Secretary-General Ban Ki-moon, and handed late Tuesday to the U.N. representative in Lebanon, Geir Pederson.
Hariri and 22 others were killed Feb. 14, 2005 in Beirut. Many Lebanese blame the attack on Syria, though Damascus has denied responsibility.
Saniora's request amounted to a formal invitation by Saniora's Western-backed government to have the Security Council establish the tribunal and bypass the Lebanese legislature.
Berri, a key member of the Hezbollah-led opposition seeking to topple Saniora's Cabinet, has defended his refusal to convene parliament under the charged political atmosphere, saying he sought to save the legislature from a possible collapse.
Last week, 70 of parliament's 128 members signed a memorandum demanding U.N. action to establish the tribunal.
On Wednesday, Saniora telephoned the U.N. chief to discuss the letter. Ban told Saniora he will take it up with Security Council members and "study all available means for establishing the tribunal," according to a statement from Saniora's office.
The opposition Hezbollah has earlier warned that seeking such international intervention would threaten Lebanon's security and stability. Its deputy leader, Sheik Naim Kassem, warned this week that a U.N.-imposed tribunal will be "a court against Lebanon and not to try the killers of Premier Hariri."