Both top candidates -- Ahmad Jarba, a tribal figure linked with Saudi Arabia, and Mustafa al-Sabbagh, a businessman who is Qatar's point man, were not able to gain half of the 115 votes of the members of the Syrian opposition early on Saturday.
Another meeting was scheduled for later on Saturday as the SNC is split into three power centers including “the Muslim Brotherhood, the Sabbagh faction, and a Saudi-backed bloc that includes Jarba.”
The foreign-backed opposition has been without a leader for months.
The meeting, which kicked off on Thursday, is the second of its kind by the troubled opposition group over the past two months to unite.
George Sabra became acting president of the SNC in April 2013, shortly after Moaz al-Khatib resigned as the group's leader.
On June 14, US President Barack Obama ordered his administration to provide the militants with weapons.
Syria crisis started in 2011 when pro-reform protests turned to a massive insurgency following the intervention of western and regional states.
The unrest which took in numerous terrorist groups from all over Europe and the Middle East is going to become one of the bloodiest wars in the recent history.
The war, which many fear is turning to a “war of hatred”, has already taken thousands of lives.
The Syrian army has conducted successful operations against the foreign-backed Takfiri militants over the past weeks.
In May, Syrian President Bashar al-Assad said militants from 29 different countries are fighting against the government in different parts of the country.