Exxon Mobil Corp. and other energy companies have joined President Donald Trump in expressing concerns over a bill to toughen sanctions on Russia, arguing that it could shut down oil and gas projects around the world that involve Russian partners.

The pushback from energy companies such as Exxon XOM, -1.61% and Chevron Corp. CHV, +0.79% — and from some companies in other industries — threatens to complicate House passage of the legislation, aimed partly at punishing Russia for what U.S. officials concluded was a campaign to interfere with last year’s presidential election. The bill breezed through the Senate last month on a 98-2 vote.