"The weather conditions and other environments today are as good as yesterday".
Interior Minister Anupong Paochinda also said the boys were in good health.
A retired Thai navy SEAL died Friday after he ran out of oxygen while placing compressed-air tanks along the exit route.
Doctors fear the children, who are aged between 11 and 16, may have contracted illnesses or infections while they were trapped underground.
A total of eight boys have now been rescued.
Narongsak said that the "same multinational team" that went into the cave on Sunday to retrieve the first four boys was deployed on Monday.
Divers took about four hours to escort the four from the ledge to the chamber, the source added.
Prime Minister Prayuth Chan-ocha visited the cave to inspect the rescue operation, with navy rescuers giving him a rousing cheer.
Divers have rescued four more boys from a vast cave system in northern Thailand on the second day of a challenging mission, as the first four rescued boys recover in hospital.
Families of the four boys who were rescued on Sunday evening have not yet seen them since they were rushed to the Chiangrai Prachanukroh hospital, about 60 miles from the cave.
After the four boys were removed from the cave, heavy rain started falling. 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.
Monday's operation took nine hours, two fewer than Sunday, with rescuers helped by the experience they have accumulated, Narongsak told a news conference punctuated with rounds of applause. Relatives were able to see them through a glass partition, the governor said.
Thailand officials have not released the names of the boys rescued, so as not to upset the parents of any child still trapped.
"The water level is not worrisome", he said, the paper reported.
Workers have been labouring around the clock to pump water out of the cave, and authorities said Monday that heavy downpours overnight did not raise water levels inside.
"As all of us said, the main thing is we still need more than 20 hours to get ready", Narongsak said.
That sense of accomplishment was also reflected in the message posted Monday night on the Thai Navy SEALs' Facebook page announcing the latest rescues. Thais have been fixated on the crisis, hoping desperately for the safe return of the boys and their 25-year-old coach, since they became trapped in the Tham Luang cave complex on June 23 because of rising waters.
But with oxygen levels inside dropping to unsafe lows and the prospect of heavy rains flooding the area completely, authorities decided they had to move quickly and take the group out through the water-filled tunnels.
The rescue operation to free a Thai soccer team from a cave is underway.
Elon Musk's Space X rocket company is testing a "kid-sized submarine" that could be sent to help boys trapped in a flooded Thailand cave.
Soldiers arrive outside the Tham Luang cave complex in the northern province of Chiang Rai, Thailand, July 8, 2018.
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