At least nine ambulances have been waiting at the site after the leader of the rescue operation earlier said the aim was to bring out all five of the football group as well as a medic and three Thai Navy Seals, who have been with the trapped boys.
Officials have generally waited hours to confirm rescues.
Health experts have given the eight who were rescued on Sunday and Monday a chocolate treat and described them as being in good spirits.
Chiang Rai Governor Narongsak Osatanakorn said Tuesday's intricate and high-risk operation began just after 10am local time and involves 19 divers. A medic and three Thai Navy SEALs who have stayed with the boys on a small, dry shelf deep in the flooded cave will also come out, he said.
"We expect that if there is no unusual condition ... the four boys, one coach, the doctor, and three SEALs who have been with the boys since the first day will come out today," he told a news conference to loud cheering.
Nargonsak said this phase may take longer than the previous two rescue missions, the longer, first missing taking 11 hours.
The eight boys brought out by divers over the previous two days are in "high spirits" and have strong immune systems because they are soccer players, a senior health official said.
Doctors were being cautious because of the infection risk and were isolating the boys in the hospital. They did get a treat, however: bread with chocolate spread that they'd requested.