MONTREUX, Switzerland—Syria and the U.S. opened a long-awaited peace conference by clashing over the fate of President Bashar al-Assad, exposing the depths of division and pessimism about any progress at the first talks in nearly three years of war.

The early sparring in Switzerland on Wednesday centered on Western demands that President Bashar al-Assad be removed from power. U.S. Secretary of State John Kerry kicked it off by insisting Mr. Assad must go.

His Syrian counterpart, Foreign Minister Walid al-Moallem, immediately challenged the notion. He accused the U.S. and its Middle East allies, particularly Turkey and Saudi Arabia, of supporting terrorist groups seeking to destabilize the Damascus regime.

However, there was a rare overture to the opposition by Syrian Deputy Foreign Minister Faisal al-Mekdad, who left open the possibility of parliamentary elections this year, a year earlier than the 2015 timeline for the polls.

Some opposition forces have called for a new parliamentary vote before presidential elections expected in June, hoping this would allow a coalition of leaders to emerge and form the foundation for a political transition away from Mr. Assad's rule.