Sheikh Moaz Alkhatib, the moderate Islamic cleric who leads the 70-member assembly, said he would be ready to meet Assad's ceremonial deputy Farouq al-Shara if Assad fulfils conditions including the release of tens of thousands of political prisoners.
"The coalition needs to convene to chart an urgent strategy after the reverberations of the initiative and seize on the momentum it has created, regardless of the reservations of some members," one coalition official said.
"The initiative is proving to the international community that Assad is not willing to compromise one millimetre and we need to take advantage of that," he added.
Thirty members of the coalition have sent a letter to its leadership demanding an emergency meeting for the whole assembly, according to coalition sources.
While a number of opposition figures have criticised Alkhatib's offer to talk to Assad's representatives, others say it could expose Assad's proposals for dialogue as hollow.
Ahead of surprise meetings last weekend between Alkhatib and the foreign ministers of Russia and Iran, Assad's main backers, the coalition abandoned its policy of refusing to talk with the Assad regime unless Assad stepped down first.
Speaking after the meetings at an international security conference in Munich, Alkhatib said neither Russia nor Iran had an answer to the 22-month-old crisis and Syrians must solve it themselves. A spokesman for the coalition described the meeting with Iran as a failure.
The coalition, formed with Western and Gulf backing last year, has a "collegiate" leadership, and Alkhatib is a first among equals, rather than outright head.
Fawaz Tello, a veteran opposition campaigner who worked with Alkhatib to defend human rights in Syria before the revolt, said the initiative could prove an astute move because it puts the onus on foreign governments to act.
"Russia and Iran and even many in the rest of the international community so far have shown no willingness to put any serious pressure on Assad to accept a political solution," Tello told Reuters from Berlin.
Syrian authorities have remained silent on the initiative, but the semi-official al-Watan newspaper said on Tuesday Alkhatib was not acceptable as a negotiator.
One of the 12 members of the coalition's politburo said Alkhatib's initiative had popular support in Syria but needed to be "politically more sophisticated".
He said the politburo, the coalition's highest decision-making body, was due to meet on February 14 to be briefed by Alkhatib but the whole 70-member coalition was likely to meet in an emergency session before then.
Senior coalition member Burhan Ghalioun, one of the few secular liberals in the coalition, said he was concerned the initiative could weaken opposition fighters on the ground.
"Lots of friendly countries or those who claim friendship for the Syrian people were waiting for this exact kind of initiative to justify their failure to deliver on military support for the revolt and the protection of civilians," Ghalioun said.
AMMAN, Jordan (Reuters) -- Members of the opposition Syrian National Coalition have called for an emergency meeting to discuss a controversial proposal by its head to negotiate with President Bashar Assad's government, opposition sources said.