WASHINGTON—Republican nominee Donald Trump disagreed Sunday with his own running mate’s call for U.S. strikes against the Syrian military over a Russian-backed offensive against Aleppo, saying the two haven't discussed the matter.

Indiana Gov. Mike Pence, Mr. Trump’s running mate, said at a vice presidential debate Tuesday that the U.S. “should be prepared to use military force” against Syria to stem the crisis caused by a Russian-backed offensive in Aleppo.

Mr....