Narongsak said earlier on Sunday the mission may take three or four days to complete.
Parents say they haven't been told which boys were taken out of the cave, and have not been allowed to visit them in hospital.
Thailand's Interior Minister Anupong Paojinda has revealed the same divers who rescued the four boys will also conduct the next operation due to their knowledge of the terrain.
Each rescue operation takes around 10 hours.
He had said fresh air tanks needed to be laid along the underwater route.
Eight boys and their coach remain trapped in the caves, with rescue operations now on hold after the first entry depleted resources.
"Today is D-Day", Narongsak Osottanakorn, head of the rescue mission, told reporters.
"This morning they said they were hungry and wanted to eat khao pad grapao", Narongsak said, referring to a Thai dish of meat fried with chili and basil and served over rice.
The boys, who are aged between 11 and 16 years old, along with their 25-year-old coach Ekkapol Chantawong, went to explore the Tham Luang Nang Non cave after football practice, but did not return home that night.
Just a few kilometres from the lush forest that covers the mountainside of the Tham Luang cave, four boys dressed in their white school uniforms shoot hoops on an outdoor basketball court in Mae Sai.
The first four rescued boys have been placed in a ward set aside specifically for the cave rescue, a source at the hospital said.
The worldwide effort to save the Thai boys and their soccer coach trapped in a cave includes divers and experts from all over the world.
Officials said it had not changed the water level in the cave but forecasters have warned rain could continue to hit the area throughout the week.
Dozens of foreign divers and other experts from around the world were brought in to help the rescue effort, working along side Thai Navy SEALs.
Authorities have so far refused to release the identities or conditions of the four who have escaped.
The rescuers are racing against time, as more rain is forecast, and the extra water would significantly complicate matters. They eventually found a dry landing spot, where they waited for nine days before being found by two British divers.
The soccer team seen in the cave last week, before anyone was rescued. "But there are caves where. explorers could go in and be trapped by rising water during like a heavy rain and trapped in an air pocket", Brick said.