A rupture in the submarine electricity cable linking to the mainland has left both islands with only a meagre reserve power supply since Tuesday.
Wattana Praekul, of the Provincial Electricity Authority (PEA) in Nakhon Si Thammarat province, said on Thursday morning that PEA engineers were having difficulties trying to repair the damaged high voltage cable because of the confined space and wet soil.
However repair work was about 70% complete and if there were no additional delays power should be restored around noon on Thursday.
Provincial governor Chatpong Chatphuti flew to Samui island by helicopter today to oversee the repairs.
Normally the holiday season Samui island, one of Thailand's major tourist destinations, would have about 20,000 tourists. That number had shrunk to about one thousand, reports said.
Power was still sporadically available on parts of the islands, but hotels and resorts were having to rely on their own generators, or candles. The wireless telecommunication network had also been knocked out.
The reserve power supply was only able to distribute electricity to one fifth of the islands' area at a time, on a two hour rotation, the PEA said.
Wanni Thaipanich, chairwoman of the association of tourism promotion for Koh Phangan, said smaller hotels were suffering as guests cancelled bookings and moved to larger establishments with their own power generators.
Mobile generators have been dispatched to major hospitals on the islands.
PTT had been asked to urgently transport fuel to both islands as there was now a fuel shortage and people were hoarding supplies. Many hotels were running out of fuel for their generators.
Samui and Phangan have a combined daily power consumption of about 90 megawatts.