Eight boys have been brought out from the cave in northern Thailand where they were trapped with four other members of the Wild Boars football team and their coach, on the second day of a daring series of rescues.

The four remaining boys and the coach, Ekaphol Chantawong, are spending a 17th night inside the cave and authorities say it is unclear whether all will be freed by the end of Tuesday.

“We are so happy that today we could rescue another four kids,” Narongsak Osatanakorn, the head of the joint command centre coordinating the operation, announced at a press briefing on Monday evening.

All four were airlifted to a hospital in the nearest city, Chiang Rai. “Now they are fine,” he said.

An elite team of 18 Thai and international divers supported by at least 80 other rescue workers entered the cave at about 11am (0500 BST) on Monday, managing to send the last of the four boys to hospital by 8pm, two hours faster than the operation on Sunday that freed the first four children.

“We had a bigger operation team and we were more skilful,” Osatanakorn said.

The next operation is scheduled to be launched by 4pm local time on Tuesday but the rescue chief said he could not guarantee the last five would be freed by the end of the day.

“I cannot answer this question right now,” he said. “It’s down to weather conditions and our plan. We’ve set a plan for four but if we want to rescue five, those responsible will have to adjust the plan. We can’t overrule the diving team because it involves safety.”

Witnesses at the cave site said the first boy was stretchered from the entrance at about 4.30pm on Monday.

Over the next two hours, three more boys were freed one by one, each stretchered from the cave, treated in a field hospital on the site then flown to the Chiang Rai hospital about 50 miles (80km) away.

At about 7pm, the official Facebook page of the Thai navy Seals – who have played a key role in the rescue – posted a message: “Two days. Eight boars. Hooyah,” it read.

The Thai prime minister, Prayut Chan-o-cha, visited the site a short time later, meeting the boys’ families.

Officials said conditions that had triggered Sunday’s operation – declining water levels in the cave, the readiness of rescuers and the physical and mental health of the stranded boys – were the same on Monday morning and the rescue had commenced five hours earlier than expected.

“The factors are as good as yesterday [and] the rescue team is the same team with a few replacements for those exhausted,” Osatanakorn said.

Asked which boys would be coming, he said: “The perfect ones, the most ready ones.”

An official from Thailand’s forestry department said water levels were still falling in the cave as thousands of pumps were operating and the site had not been substantially affected by the intermittent rain of the past 48 hours. “The water level is not worrisome,” he said.

It is unclear whether the parents of the group have been informed yet which of their sons has been freed.

Facebook Twitter Pinterest The Thai prime minister, Prayut Chan-o-cha, meets some of the trapped boys’ family members. Photograph: Thai Government Spokesperson'S Office Handout/EPA

Doctors quoted by Thai media said the delay was to manage the mental health of the parents whose children are still inside the cave, as well as to ensure the boys can be tested for any diseases they might have picked up inside its dank, flooded interior.

Authorities said on Monday a medical team was assessing whether to reunite the boys with their parents soon.

“The medical team is considering whether to let closest relatives visit them,” Osatanakorn said. “It could be a visit through transparent glass rooms. We are discussing this with doctors at the hospital.”

The freed boys could not yet be officially named due to “doctor-patient confidentiality”, he said.

A difficult journey still awaits the last four boys and Chantanwong but authorities appeared more relaxed than in previous days after the success of Monday’s extraction, which was announced to applause from journalists and volunteers.

Preparations are under way to manage the mental health of the boys once they are all freed. Students and teachers at Maesaiprasitsart school, attended by many of the children, have been given instructions to avoid “talk that hurts [the boys’] feelings”, said Thongyaud Kejorn, a teacher.

The boys will not have to sit an exam scheduled for next week, he added. “They will not have to follow the normal schedules.”

Kittichok Kankeaw, a teammate of Nattawut Takamsai, one of the trapped boys, said he would try to assist his friend to catch up at school. “I can help him with his homework,” he said.

Osatanakorn said the first four boys to be freed had woken up in good condition and were asking to be served khao pad krapow [basil chicken with rice]. But doctors were still restricting their diets. “They can eat normal food now, but only ‘fluid’ food like diluted porridge,” he said.

Storms are predicted for Tuesday but similar forecasts for the past two days have failed to deliver heavy rain that might have scuppered the rescue.

Gen Buncha Duriyaphan, an army commander involved in the operation, said he had been asking Pra Pirun, the god of rain, for three days’ reprieve to conduct the operation. He said praying for an extension may be viewed as indulgent. “If I ask for more, he might not grant it,” he said.

Additional reporting by Jacob Goldberg and Veena Thoopkrajae

