The group went into the Tham Luang cave more than two weeks ago.
He said the health of the five people remaining in the cave was "still good" and rescuers would resume an operation to retrieve them in about 20 hours' time.
"The mission has resumed", a government official closely involved in the mission told Reuters, declining to be identified.
British divers found the 13, huddled on a muddy bank in a partly flooded chamber several kilometres inside the complex, on Monday last week.
The Thai authorities have been pumping out water from the cave system ever since locating the missing soccer team, but that wasn't enough to remove all the water.
The extraction of those remaining is expected to take another two to four days, depending on conditions.More news: NATO Braces for Trump Visit, But Fears May Be Overplayed
The soccer team had been trapped in the underground cave network since June 23, with flash floods causing water levels to rise, making it hard to get out.
Asked whether the remaining four "Wild Boars" team and their coach would come out at the same time in the next rescue effort, he said: "It depends on the plan".
A video published by the Thai PBS channel earlier on Monday also showed a person on a stretcher - most likely the first boy to be rescued on Monday - being transferred to a helicopter.
Officials said on Sunday that it may "take days" to rescue all 12 boys and their coach.
The extraction of the four on Monday followed a similar pattern to the previous day, with the youngsters emerging in quick succession just before nightfall after navigating a treacherous escape route of more than four kilometres.
Thai authorities said the rescuers, who were fully equipped, had spent five hours from the entrance of the cave to reach the children and six hours, including a break, to bring them back.
First of all, four of the boys were successfully extracted from the cave system. There was no word on the condition of the fifth boy brought out earlier on Monday.More news: Buffon ready to fight for PSG place but not targeting Champions League
Their escape led to an explosion of jubilation on social media in Thailand as the rescued boys were rushed to hospital.
Authorities have been rushing to extract the boys, ages 11-16, and their coach from the cave as the annual monsoon bears down on the mountainous region in far northern Chiang Rai province.
After the ambulance was seen leaving the complex at around 5 p.M. Monday, a helicopter took off. Authorities have said helicopters were ready to take cave evacuees to a hospital. Still, the four were undergoing medical checks in a hospital in the provincial capital and were not yet allowed close contact with relatives due to fear of infections. That said, Musk's effort, while laudable, might not be needed for this particular rescue.
Thai officials have confirmed that they are prioritising the weaker boys first, in order to ensure they get quick treatment.
"We've used all the oxygen", Osatanakorn told reporters.
"I'm hoping for good news", he said.
They are the second batch to undertake the perilous journey out of Tham Luang cave in Mae Sai district in Chiang Rai.More news: Ronaldo signs for Juventus from Real Madrid
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