The coalition said on Wednesday it would only take part in peace talks that the United States and Russia are planning if a deadline was set for a settlement that would force Assad to leave power.
Russian Foreign Minister Sergei Lavrov said the coalition gave the impression it was "doing everything they can to prevent a political process from starting ... and achieve military intervention".
"We consider such approaches unacceptable," he said.
Russia, which has been Assad's most powerful protector during the conflict that has killed more than 80,000 people in Syria, has repeatedly said that his exit should not be a precondition for a political solution.
"The National Coalition is not prepared to take part in the conference without preconditions. These conditions are impracticable. And in general, nobody should be throwing ultimatums around," Lavrov said at a news conference after talks with Cuban Foreign Minister Bruno Rodriguez Parrilla.
The coalition "has no constructive platform", he said.
"The only thing that unites them is the demand for Bashar al-Assad's immediate exit. But everyone, including our Western partners, understands that this position is unrealistic."
Lavrov said the coalition was "not the sole representative of the Syrian people" and that groups with members inside Syria - including the National Coordination Body, whose representatives have visited Moscow several times - were ready to take part in the proposed peace conference.
"I hope that sensible forces among the Americans and Europeans will clamp down on those who indulge in such unacceptable and aggressive approaches by the National Coalition and who try to cast this coalition as the sole structure with which the Syrian government should talk," he said.
Lavrov and U.S. Secretary of State John Kerry said on May 7 they would seek to bring Syrian government and opposition envoys together as soon as possible at an international conference aimed at ending the 26-month-old conflict. No date has been set.
Under pressure to broaden their Islamist-dominated ranks to improve prospects for peace talks, the Syrian opposition agreed on Thursday to admit a liberal bloc after seven days of marathon talks that exposed deep rifts in its ranks.