"We remain committed to General Aoun as long as he remains the candidate," Hassan Nasrallah said in a televised address. "This commitment is based on mutual trust."
Nasrallah added however that Hezbollah would not force other political allies to back Aoun, 82.
"We don't impose our decision on anyone," Nasrallah said.
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Lebanon has been without a president since May 2014, when the mandate of Michel Sleiman expired.
Since then the country's Christians, Sunni and Shiite Muslims and Druze cannot agree on a candidate as the neighbouring war in Syria further polarises parties.
Several previous votes have failed to produce a president and parliament is due to convene on February 8 for another attempt.
Under Lebanon's 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.