The Tongan government confirmed three deaths, including that of a British woman, saying it had been hit by an "unprecedented disaster."
Aid efforts have been hampered by ash continuing to fall from the volcano.
The severed Tonga cable runs to Fiji, where it intersects with the trans-Pacific Southern Cross Cable, connecting Tonga to Australia, the US and the rest of the world.
many tongans abroad have been waiting to hear news from loved ones after the internet and phone services were affected.
The UN said it was unclear if personnel could be sent to assist, but that supplies like water and food could be delivered as the main island's port remained viable.
While some telephone networks within the country had been restored and Australia and New Zealand were assisting with satellite calls, communications remained limited, particularly with outer islands.
"We are just going through our preparations for the repair operation to start possibly next week," he told the Guardian.
Preliminary testing indicated a break in the 827km-long Tonga cable about 37km offshore of Tonga's capital, Nuku ’ alofa.
The country's domestic communications cable runs from the capital north to Pangai and Neiafu.
According to the Tongan government, 36 people live on Mango and 69 on Fonoi.
Tongan rugby players living in the UK have spoken of their distress at not being able to communicate with family members after the tsunami.
"it's really tough, sleep-wise and not knowing what's going on; it's hard for me to focus and try to get myself ready for training and rugby."
Former All Black Fekitoa, born and raised on the island of Ha'apai, said he also hadn't been able to contact his mother and family.
He set up the fundraising page to "send essential products" via containers from Auckland in New Zealand.
His Coventry teammates as well as the wider UK rugby community had been "very, very supportive", he said.
"I'm amazed at how many people got together and showed support, and hopefully we can help a few families back home."
aerial images prepared by the new zealand defence force for the tongan government have been leaked online and show some areas have had "catastrophic" devastation inflicted by the tsunami and volcanic eruption while others show parts of the country that appear unscathed.
The Guardian has confirmed the provenance of the photos.
A distress sign was detected from Mango Island on Monday by the UN prompting concern for inhabitants.
"Clearance operations by shovel and wheelbarrow were under way on the SE end of the runway.
Little has been heard from Tonga since the eruption of Hunga Tonga-Hunga Ha'apai volcano and subsequent tsunami on Saturday, after the Pacific nation ’ s main communication cable was broken.
It may be weeks before the cable can be repaired, due to difficulty getting the repair ship from Papua New Guinea to Tonga, and safety concerns for the crew of the ship, who would be operating in waters not far from the volcano, meaning Tongans around the world may be forced to wait weeks for regular contact to resume.
On Tuesday, New Zealand's ministry of foreign affairs and trade said there had been two confirmed deaths in Tonga from the disaster, one of which was a British national.
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