With the parliament divided between two powerful blocs, one centered around the Hezbollah movement and the other opposed to it, the outcome had been expected.
The parliament will now hold a second vote on April 30, in which the winning candidate will only need a simple majority of 65 votes.
In Wednesday's vote, 124 of the parliament's 128 members were present, with 48 casting their ballots for Samir Geagea, the candidate backed by the March 14 movement opposed to Hezbollah.
Observers had predicted Geagea would fail to win the two-thirds majority required because of his fierce anti-Hezbollah stance.
Members of the rival March 8 bloc centered around the powerful Shia Hezbollah movement have not officially backed a candidate, and most of its members appeared to have submitted blank ballots -- 52 in total.
A second candidate, Henri Helou, who is backed by members of a small bloc of independents and centrists, won 16 votes.
One vote was submitted for former president Amine Gemayel, and seven votes were deemed void.
Hezbollah's bloc, which holds 57 seats in the parliament, has yet to announce its support for a candidate.
But its supporters strongly oppose Geagea for his anti-Hezbollah stance, while other critics point to his convictions for crimes committed during the country's 1975-1990 civil war.
Several lawmakers marked their ballots with the names of political figures Geagea was convicted of killing during the war.
Lawmakers must pick a replacement for President Michel Sleiman before his term ends on May 25, but the political class remains deeply divided over the war in neighboring Syria.
HH/HH