British charity worker Angela Glover is the first confirmed death from the natural disaster, after an underwater volcanic eruption sparked a tsunami on Saturday and blanketed the Pacific nation in ash.
New Zealand officials believe three people have been killed.
A Telstra spokesman told AAP on Tuesday teams across the business were working with Digicel Pacific to find a satellite communications solution.
"We're now working alongside DFAT to get the equipment shipped in order to connect with one of the forthcoming planned RAAF flights," the spokesman said.
"Once the plane arrives in Tonga, our team will work with the Digicel team to get the satellite equipment working."
A detailed request for assistance is expected to come out of a cabinet meeting in Tonga, Foreign Minister Marise Payne said.
All Australians have been accounted for in Tonga following the disaster.
There are normally about 300 Australians living in Tonga, but the number is estimated to be lower due to COVID-19.
HMAS Adelaide is ready to take humanitarian supplies including engineering and medical personnel and equipment, as well as helicopters to aid with distribution.
The supplies will be deployed as early as Wednesday and the ship will take around five days to reach Tonga from Brisbane.
Two more surveillance flights - a P-8 and C130 - departed Australia on Tuesday morning.
New Zealand is sending the HMNZS Wellington and HMNZS Aotearoa.
Pacific Minister Zed Seselja said critical supplies such as food and water as well as communications and clean-up equipment will be sent on a C-130 plane once the airport in Tonga is able to reopen.
"There is still a significant amount of ash at the airport. It was hoped the airport might open today, but that's more likely now to be tomorrow," Senator Seselja told the Nine Network.
"We've offered $1 million in assistance at the moment, we're looking to hear back from the Tongan government in some more specific detail."
Initial data from a surveillance flight has come through and was shared with Tonga, with on-ground efforts also being carried out by Tongan authorities.
Officials have warned the death toll from the volcanic eruption and tsunami is only set to grow, as damage assessment begins.
The deputy head of mission at Tonga's high commission in Australia, Curtis Tu'ihalangingie, said there was still uncertainty about the level of damage, but basic supplies were needed.
"At this point (Tonga needs) water and also masks," he said.
"The country was covered with volcanic ash and this is very alarming and dangerous, not only for young children but for everyone."
A major underwater telecommunications cable was damaged in the tsunami, and is expected to take at least two weeks to repair.
The high commission still does not have direct communication with the Tongan government.
With Tonga enforcing strict border measures to keep coronavirus cases out of the country, there are fears international aid efforts could lead to the Pacific nation losing its COVID-free status.
"As much as we are going to send assistance, we will still need to follow the COVID-19 protocols to keep the people in the population safe, rather than us setting a system and there's a tsunami of COVID hitting Tonga," Mr Tu'ihalangingie said.
"We hope to maintain that and we're very appreciative of the understanding of the Australian government and partners."
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