The two men were named as Angelo Bien Rafael Cortez, 29, and Noah Ibay, 40.
Kusoldharm Phuket Foundation rescue workers were called to help search for the two men at 5:30pm.
The search continues today, with lifeguards and police scouring the coast at Patong Beach to the north and Karon Beach to the south.
Mr Cortez and Mr Ibay were among a group of 13 tourists who came to Phuket together, Patong Surf Life Saving Chief Somprasong Sangchart told The Phuket News.
The group went swimming at the beach, but Mr Cortz and Mr Ibay soon disappeared among the waves, he added.
Two other men, John Jerard Tanghal, 30, and Tanghal Paciano Jose, 51, needed rescuing and were taken to Patong Police, where they are now safe.
The search from Mr Cortez and Mr Ibay by boat was delayed this morning due to bad weather, Mr Somprasong said.
“But we will resume it as soon as we can,” he added.
The tourists' disappearance and surf rescues yesterday follows the International Surf Lifesaving Association (ISLA) issuing a surf danger warning (see here) and a weather warning being issued for Phuket and the Andaman coast, including an advisory from the Phuket Marine Office calling for all small boats to stay ashore. (See story here.)
Additional reporting by Eakkapop Thongtub