In a statement on Wednesday afternoon, the Tongan Government said clean-up and damage assessments are ongoing, while emergency supplies are being distributed.
Work to clear the airport runway continues and is expected to be complete today.
More information on the extent of the damage has started trickling in from the country, which has been largely cut off from the outside world since the disaster with communications networks down.
According to the Tongan Government, international mobile phone network provider Digicel has set up an interim system on Tongatapu using the University of South Pacific's satellite dish which may allow a 2G connection to be established today.
Meanwhile, the New Zealand Government said two Navy vessels sent to Tonga with support and expert personnel included divers who could assess the wharf where there is significant damage. There is also seabed damage.
About 150 people will be evacuated from two of the smaller islands - Mango and Fonoifua - where damage has been most severe.
Foreign Affairs Minister Nanaia Mahuta and Minister of Defence Peeni Henare told media this afternoon that the arrival of HMNZS Wellington and HMNZS Aotearoa has been approved - while a C130 Hercules is also on standby once the airport runway is clear.
A second NZDF P3 Orion surveillance flight is also being conducted today. This flight will include a survey of Fiji's southern Lau Islands, at the request of the Government of Fiji, to check for potential tsunami damage.
New Zealand is continuing to assess Tonga's water transport logistics capabilities for the transport of water from HMNZS Aotearoa.
Mahuta said a significant area of need was to provide water - and New Zealand's support would help with capture of the water resource there.
A total of $1 million in financial support had been provided, she said.
There has been no significant damage to the airport runway and it is believed the clean-up of the runway would be completed by the end of this week.
On Covid-19 protocols, Mahuta said the conversations had been around contactless delivery and how that could take place.
Mahuta said the humanitarian efforts would be operated within a Covid context.
The pandemic presented a challenge in "all sorts of ways" but some activities did not involve any contact between people, like assessment of the seabed.
According to Henare, New Zealand's Hercules was on standby "as we speak".
Henare said the number one priority for the Navy ships when they arrive in Tonga would be how water could be supplied.
On repatriation flights from Tonga, Mahuta said consideration had been given to it but nothing had been confirmed yet.
New Zealand is very reliant on the assessment of Tonga and what they see as a response for their people.
New Zealand stands ready to assist in any way that would be helpful for them, Mahuta said.
Three fatalities confirmed
No further deaths have been reported after the Tongan Government last night confirmed three people had been killed in the disaster.
British national Angela Glover, 50, was the first fatality reported; as well as a 65-year-old woman from Mango Island and a 49-year-old man from Nomuka Island.
Henare told Newstalk ZB earlier today that aircraft could not yet land on the main airport runway on Tongatapu due to ash.
It is expected to open some time tomorrow morning - allowing RNZAF aircraft to bring in essential items and for aid to land safely.
He spoke of the lengths members of the public have gone to, to help clear the runway.
"The people in Tonga are, in some parts, sweeping the runway by hand, so it's taken a bit of time," he told Newstalk ZB's Tim Dower this morning.
Henare acknowledged earlier that the Tongan Government was also conscious of the potential of Covid being brought to their shores and wanted to protect its people from the virus as well.
Tonga is one of a few countries in the world and the Pasifika region that remains Covid-free.
Advice for Tongans in NZ trying to contact loved ones
Meanwhile, the Ministry of Foreign Affairs and Trade is advising people in New Zealand who have lost contact with relatives in Tonga to register their names via the NZ Red Cross.
The charity has activated its Restoring Family Links system in Tonga, which may help Tongan Kiwis to connect with family members back home.
Relatives do not have to be New Zealand citizens.
Anyone who is a Kiwi citizen living in New Zealand and requires consular assistance - or has concerns about a New Zealand citizen living in Tonga - can contact the New Zealand Consular Emergency phone line on: +64 99 20 20 20.
The Red Cross NZ has also started a Pacific Tsunami Appeal for anyone wishing to donate.
"Our Pacific neighbours urgently need your support as they cope with the devastating impact of Hunga-Tonga-Hunga-Ha'apai volcanic eruption."
