Divers found the group of seven students and their instructor in an air pocket 36 hours after they were first reported missing in the cave near the town of Gaumois on Wednesday.
On Friday night rescue teams had to delay their efforts to bring out the potholers after water-pumps were unable to cope with the volume of water in the flooded caves and broke down.
A spokesman said the five men and three women were all safe and they were still confident of freeing them.
Divers found the group of seven students and their instructor in an air pocket 36 hours after they were first reported missing in the cave near the town of Gaumois on Wednesday.
The group became trapped by rising underground floodwaters following heavy rain.
The potholers are about 100 metres from the entrance to the caves, and are being given food, water and medical attention. All are said to be tired but safe and dry.
Rescuers had hoped they would be able to free the cavers by mid-afternoon on Friday.
New attempt
Several hundred rescue experts from Switzerland and France are at the site in Goumois, 20km (12.5 miles) from the French-Swiss border.
In a bid to lower the water level, the rescuers have deployed several powerful pumps, so that divers can get further inside the cave.
But the pumps apparently could not cope with an unexpected surge in underground water levels.
"Our pumps are getting flooded out... Only three out of 12 are working at the moment," said Eric Zipper, one of the rescue workers.
Rescue workers were trying to dry a section of the caves in order to bring the group back to the surface.
Mr Zipper said a new attempt to bring them up would be made around midnight (2200 GMT).
Warnings 'ignored'
Rescuers began arriving at midnight on Wednesday after the alert was given.
Experts say the cavers should be brought out the way they came, although rescuers are also digging a hole into the tunnels from above.
The potholers are all in their 20s, seven of them are student social workers from a Zurich college, while one is a teacher.
They had gone on the trip to help develop their ability to face challenges in their careers.
French television reported that the group had ignored poor weather conditions and warnings from locals not to venture down the cave.