A Reuters witness said a sixth and seventh person had been carried from the cave on stretchers, which means most of the group of 13 have now been rescued.
A Royal Thai Navy official later confirmed a fifth boy had been rescued.
A mission to rescue a group of boys and their soccer coach trapped in the flooded cave since June 23 resumed hours earlier.
The first four boys, from the group of 13, including the coach, were rescued on Sunday.
An operation to rescue a group of Thai boys and their soccer coach trapped in a flooded cave resumed on Monday (local time), say several officials with knowledge of the operation at the Tham Luang cave in the northern Thai province of Chiang Rai.
The operation to rescue the remaining eight boys - some as young as 11 and weak swimmers - and the coach was called off at nightfall yesterday until today to give the divers time to replenish oxygen supplies and ensure all preparations were complete.
The chief of the mission has said the four rescued boys were fine and were being kept apart from relatives because of concerns over infection.
"We are using more personnel than yesterday," the chief of the rescue mission said.
Names of the rescued boys had not been released out of "respect for those families whose sons are still trapped inside", he said.
Thirteen foreign divers and five members of Thailand's elite navy SEAL unit guided the boys to safety through narrow, submerged passageways that claimed the life of a former Thai navy diver on Friday.
"Today was the best day, the best situation in terms of the weather, the health of the boys, our water management for our rescue effort," the head of the rescue operation, Narongsak Osottanakorn, told a news conference.
"Today we managed to rescue and send back four children to Chiang Rai Prachanukrua Hospital safely."
A helicopter flew the four boys to the nearby city of Chiang Rai, where they were taken by ambulance to the hospital.
Their ordeal has drawn huge media attention in Thailand and abroad, and getting the boys out safely could be a boost for Thailand's junta ahead of a general election next year.
"Today is D-Day," Narongsak had earlier told reporters.
Bursts of heavy monsoon rain soaked the Tham Luang Cave area in northern Chiang Rai province on Sunday and storms were expected in coming weeks, increasing the risks in what has been called a "war with water and time" to save the team.
The boys, aged between 11 and 16, went missing with their 25-year-old coach after soccer practice on June 23, setting out on an adventure to explore the cave complex near the border with Myanmar and celebrate a boy's birthday.
"CONDITIONS MUST BE STABLE"
"If we wait and the rain comes in the next few days we will be tired again from pumping and our readiness would drop. If that's the case, then we have to reassess the situation," he said.
"We can only carry on the operation once we are ready and this will be done soon, because the air tank and other systems have to be reinstalled," he told reporters later.
"...I can't give you an exact number but it should be more than 10 hours but not exceeding 20 hours. The conditions must be stable like today before we can continue the operation."
An Australian doctor checked the health of the boys on Saturday night and gave the all-clear for the operation to proceed.
The boys were discovered by British divers Richard Stanton and John Volanthen on Monday.
Of the 13-strong foreign dive team - mainly from Europe - three escorted the children, while the remainder were positioned along the dangerous first kilometre stretch, where the boys had to navigate through submerged passageways in some places no more than two feet (0.6 metre) wide.
The area outside the Chiang Rai hospital was cordoned off by police. Down the street, vendors were told by loud speaker to "keep off the road" and to "not obstruct the transfer mission".
Prime Minister Prayuth Chan-ocha, leader of the military junta that seized power in 2014, planned to visit the cave site on Monday, a government spokesman said.
His visit with relatives and rescue officials last week was criticised by some Thais as opportunistic as his government faced pro-democracy protests in the capital Bangkok in recent months.
A former member of Thailand's elite navy SEAL unit died during a dive on Thursday night, a grim turn in what began two weeks ago as an outing to celebrate the birthday of one of the boys.
Up on the hill, where rescuers are seeking alternative routes down into the cave, another accident occurred when a vehicle skidded off a dirt track, seriously injuring several people, authorities said.
Billionaire entrepreneur Elon Musk tweeted that a team from his rocket company SpaceX in Los Angeles is building a mini-sub to help with the rescue.
"Got more great feedback from Thailand. Primary path is basically a tiny, kid-size submarine ... Light enough to be carried by 2 divers, small enough to get through narrow gaps. Extremely robust," Musk tweeted, adding that it would take eight hours to construct and 17 hours to transport to Thailand.
The Thai defence ministry said a team from a Musk firm with drilling and exploration know-how should reach the cave on Sunday.
