The presidential vacuum is the longest since the end of Lebanon's civil war in 1990.
"Speaker of the House Nabih Berri postponed on Wednesday the presidential election session to April 2 due to lack of quorum," his office said.
Only 55 of the parliament's 128 members were present, less than the required two-thirds quorum.
Lebanon has been without a head of state since Michel Sleiman's term expired on May 25, 2014.
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The position is largely ceremonial and presidential powers have been significantly reduced in recent years.
In the absence of a head of state, executive powers fall to the government, led by Prime Minister Tammam Salam.
Lebanon's political factions are split between supporters and opponents of embattled Syrian President Bashar al-Assad, causing a stalemate over the choice of president.
Although several candidates have been announced, Lebanon's parties have insisted on reaching a consensus on the candidate, which they have yet to do.
As part of Lebanon's multi-confessional system of government, the presidency is traditionally held by a Maronite Christian, while the prime minister is Sunni Muslim and the speaker is Shiite.