WASHINGTON—President Trump issued the second veto of his presidency, refusing to sign a congressional resolution that would have ended America’s role in the Saudi-led war in Yemen.

“This resolution is an unnecessary, dangerous attempt to weaken my constitutional authorities, endangering the lives of American citizens and brave service members, both today and in the future,” Mr. Trump said in a statement on Tuesday. “Apart from counterterrorism operations against al-Qa’ida in the Arabian Peninsula and ISIS, the United States...