SEOUL—North Korea is thought to be developing a new submarine capable of launching nuclear-armed ballistic missiles, a senior South Korean lawmaker said, signaling an increased threat to U.S. and allied forces while raising doubts about the regime’s pledges to disarm.

Evidence gathered by South Korea’s military suggests Pyongyang is working on the submarine on its east coast, said Kim Hack-yong, who chaired the legislature’s defense committee until his term ended a few weeks ago. Mr. Kim, who belongs to a conservative opposition...