A 28-year-old army officer on Wednesday sued President Obama over the legality of the war against the Islamic State, setting up a test of Mr. Obama’s disputed claim that he needs no new legal authority from Congress to order the military to wage that deepening conflict.

The plaintiff, Capt. Nathan Michael Smith, an intelligence officer stationed in Kuwait, voiced strong support for fighting the Islamic State but, citing his “conscience” and his vow to uphold the Constitution, he said he believed that the conflict lacked proper authorization from Congress.