Lebanon has been without a president since May 2014, when the mandate of Michel Sleiman expired, because the country's Christians, Sunni and Shiite Muslims and Druze cannot agree on a candidate.
Under a power-sharing agreement, the president is always drawn from the Maronite Christian community, the prime minister is a Sunni and the parliament speaker a Shiite.
Speaker Nabih Berri scheduled a new session for January 7 after the required two-thirds of MPs -- 86 out of 128 -- was not reached, the National News Agency reported.
Signup to our newsletter and follow us on Facebook and Twitter!
Only 45 lawmakers showed up.
A tentative consensus had seemed to emerge early this month on Frangieh, but his chances dimmed after Wednesday's failed vote.
Daily newspaper Al-Akhbar, close to powerful Shiite movement Hezbollah, said the party would not accept any candidate other than Michel Aoun, head of the Free Patriotic Movement.
The FPM is allied with Hezbollah in the March 8 coalition, opposed to the pro-West March 14 alliance.
Ironically, Hezbollah militiamen are fighting in neighbouring Syria's civil war on the side of Assad.