MANILA — The Philippine government said on Monday that it had promised Vietnam a “fair and thorough” investigation into the deaths of two Vietnamese fishermen as they were being pursued by the Philippine Navy over the weekend.

The fishermen died from gunshot wounds on Saturday as they fled a navy patrol boat about 40 miles off the city of Bolinao in the northern province of Pangasinan, the Philippine authorities said. A police report said that the navy had fired warning shots at their vessel, and that the boats had then collided.

The Philippine foreign affairs secretary, Alan Peter Cayetano, discussed the episode hours later with his Vietnamese counterpart, Pham Binh Minh, at an informal meeting of Southeast Asian foreign ministers in New York, where they were attending the United Nations General Assembly.

“We would like to offer our sympathies over the unfortunate loss of life and give you our assurance that we will conduct a fair and thorough investigation,” Mr. Cayetano told Mr. Minh, according to a statement released Monday by the Philippine Department of Foreign Affairs.