Hours before a Russian and Turkish-brokered cease-fire was to take effect across Syria early Friday, one of the country’s most powerful rebel groups rejected the deal, upending the latest effort to end the nearly six-year war.

The rebel group Ahrar al-Sham said late Thursday that it had unspecified reservations over the cease-fire, hammered out by Turkey and Russia as part of a road map to peace talks between the Syrian government and the opposition. Though the cease-fire officially began at midnight, clashes broke out between...