"We welcome the coalition but we need to have a comprehensive strategy to address the underlying cause: Assad and Assad's brutality," said Najib Ghadbian, the Syrian National Coalition's representative to the United Nations.
"The war on ISIL will not succeed until the Security Council takes a comprehensive action," said Ghadbian, referring to the Islamic State group which now holds large parts of Syria and Iraq.
De Mistura is seeking to win Assad's backing for a plan to "freeze" fighting in the northern city of Aleppo, which is divided into regime and rebel-held areas.
The freeze would allow for deliveries of humanitarian aid and lay the groundwork for peace talks, but there has been little concrete progress on the proposal first raised in October.
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"If this is not working, we should not waste time," Ghadbian told journalists.
Next Month, Syria will begin its fifth year of war that has brought about one of the world's worst humanitarian crises.
At least 210,000 people have been killed and close to 12 million Syrians have been displaced including 3.8 million who have fled to neighboring countries.
Syria's opposition and the regime agreed in 2012 to the Geneva communique, which calls for a political transition to end the violence, but there has been disagreement on Assad's role in the transition.
Assad has long maintained that he should be a partner in the coalition fighting IS militants and sought to portray the US-led fight against the extremists as vindication of his own military campaign.
Ghadbian admitted that Assad had shown staying power, but was becoming increasingly reliant on Iran and Hezbollah to supply him with fighters, and on Russia to buffer him from international pressure.
"His forces are shrinking and there is more dependance on foreign elements," he said.