He said experts on a specialised ship are splicing the cable back together and hope to be finished by Friday afternoon, at which point they can run tests and, barring complications, fully restore the internet over the weekend.
Piukala said it had identified an oil tanker that was in the area when the cable was cut and would work with port authorities and police to determine whether there had been an act of negligence.
He said the repairs are estimated to cost over US$1 million ($1.4m), money the company, which has the government as its major shareholder, can ill afford.
Piukala said he hopes Tonga and other island nations might get together to share the costs of a joint backup plan in the future.
"We don't need a rocket scientist to tell us we need a better plan," he said. "It's a question of funding. The cost of a backup is huge, and for a country like Tonga, we don't have the luxury of money to put aside for a disaster like this. Other priorities are more urgent."
Tonga is home to just over 100,000 people. It exports some agricultural goods but also relies on external aid and remittances from abroad.
Piukala said its first priority had been to restore internet access to critical government agencies and industries like airlines and banks. He said social media was a lower priority.
"We understand people need Facebook, but we cannot talk about luxury things when we are stranded on an island without any food," he said.
Katie Silcock, the general manager of Scenic Hotel Tonga, said it was not able to process credit card payments for several days last week and had some guests cancel, but by Monday, as a priority customer, had its internet fully restored. She said many smaller operators were still without internet access and their businesses were suffering as a result.
- AP