European governments are examining whether U.S. President Donald Trump can force them to pay more for prescription medicines, after he issued an executive order to lower U.S. drug prices, roiling the global pharmaceutical industry.

Trump signed an executive order on May 12 aimed at lowering drug prices to better match what other countries charge.

Rather than cutting prices there, many firms would raise them abroad and perhaps pull out of some countries altogether, meaning Mr Trump’s policy would shrink their businesses while doing little to lo...