U.S. Secretary of State Rex Tillerson ramped up pressure Tuesday on Southeast Asian nations to shut down North Korean front companies, seeking cooperation on sanctions enforcement from longtime allies despite recent friction.

Mr. Tillerson visited Thailand and Malaysia after an Asian security summit in the Philippines at which North Korea flatly rejected any bid to force negotiations over its growing nuclear deterrent and said those weapons weren’t targeted at any other nation than the United States.

North Korea launched two missiles last month that officials said would be capable of striking the U.S. mainland, which was followed last Saturday by new sanctions on Pyongyang by the United Nations Security Council, the toughest yet on North Korea.

Mr. Tillerson is the most senior U.S. official to visit Thailand since the military seized power in a 2014 coup d’état, and also the most senior U.S. official to visit Malaysia since U.S. investigators began probing an alleged multibillion-dollar misappropriation from state-owned fund 1Malaysia Development Bhd. around two years ago.

Malaysia’s relations with North Korea were shaken after Kim Jong Nam, the half-brother of North Korea’s leader, was killed in broad daylight in a Kuala Lumpur airport in February. South Korean intelligence officials believe the killing was orchestrated by Pyongyang. North Korea has denied any connection with the killing.