Both men have doubted the wisdom of a long-term American military commitment in the country. Both have complained that Saudi Arabia expects the United States to bear the burden of a costly war against President Bashar al-Assad. Both have viewed Syria primarily through the prism of combating the Islamic State.

Though Mr. Trump’s aides made much of his order to fire Tomahawk missiles at Mr. Assad’s airfields last spring — an order that Mr. Obama famously refused to give four years earlier — it was the exception that proved the rule.

Mr. Trump, a former senior adviser said, does not believe that Syria’s civil war is a vital national security interest of the United States. Neither did Mr. Obama, which is why he initially rebuffed proposals to funnel weapons to the rebels in Syria or to impose a no-fly zone over parts of the country.