Riad Hijab, head of the opposition High Negotiations Committee (HNC), said Syrian civilians were in urgent need of protection from President Bashar al-Assad's regime, in a statement released on Wednesday night.
He called for American support to "establish peace in our region and to find fair and swift solutions for the threat of terrorism... especially the state terrorism practiced by the Syrian regime against the Syrian people," Hijab said.
The United States leads an international coalition conducting air strikes in Syria against the Islamic State jihadist group.
Washington also supports certain rebel groups fighting the Russian-backed Assad regime.
Hijab congratulated Trump on his election victory and urged him to provide "the fastest and most efficient means to protect civilians".
The conflict in Syria has left some 300,000 people dead since anti-regime protests in 2011 triggered a brutal government crackdown that has prompted accusations of war crimes.
Syrian rebels have criticised President Barack Obama for not intervening militarily against the regime.
In an interview with the New York Times on March 26, Trump said he thought "the approach of fighting Assad and ISIS (IS) simultaneously was madness, and idiocy".
"You can?t be fighting two people that are fighting each other, and fighting them together. You have to pick one or the other," said Trump, who has also pledged to improve America's ties with Assad's main backer, Russia.
Damascus has not officially reacted to the Republican candidate's victory in Tuesday's election, but pro-regime commentators have welcomed the result.