WASHINGTON—Opening-round talks to remake the North American Free Trade Agreement revealed early fissures dividing the U.S. from Mexico and Canada, including a Trump administration proposal to require a “substantial” portion of autos and auto parts produced under the pact be made in the U.S.

The renegotiation of the trade deal, which was one of President Donald Trump’s main campaign promises and a key pillar of his “America First” agenda aiming to revive U.S. manufacturing and reduce the country’s trade deficit, is likely...