The "high-speed" operation was launched despite the risk of another eruption.
Relatives waited anxiously for the mission's return after earlier attending a blessing near the island.
The bodies of eight people are thought to be on the island. Eight others have already been confirmed dead and 20 are in intensive care with severe burns.
Police say the operation is going to plan but is taking more time than expected due to the protective equipment the team are wearing, which they say "can be restrictive and heavy but is necessary".
Weather and sea conditions and conditions on the island were good, they said.
Some 47 visitors from around the world were on the island when it erupted. Twenty-four were from Australia, nine from the US, five from New Zealand, four from Germany, two from China, two from the UK, and one from Malaysia.
GeoNet, New Zealand's geological hazard information site, said on Thursday there was a 50-60% chance of another eruption within the next 24 hours.
But families of the victims have been growing increasingly desperate for the bodies to be recovered.
"We are now living with a growing sense of desperation to bring home those that we know are there," Whakatane Mayor Judy Turner told reporters.
"The frustration of those families most affected is completely understandable."
Specialists from the New Zealand Defence Force went to the island on Friday morning to try to recover the bodies.
The team, kitted out with protective clothing and breathing apparatus, was flown from a naval frigate to the island on Friday morning local time.
If the volcano erupts while they are on the island they could face the danger of magma, superheated steam, ash and rocks thrown at high speed, volcanologists say.
During the operation, a geologist is analysing real-time data to assess whether the mission needs to be aborted.
Deputy Police Commissioner Mike Clement told reporters that recovery efforts were going to plan but cautioned that there were "many things that could go wrong".
The operation is expected to take a few hours.
The fast recovery means there is less time to collect the evidence needed to ensure that the bodies are properly identified.
All of the bodies are within 200m (656ft) of each other, according to the New Zealand Herald.
Many of the survivors are still in intensive care. Some have been unable to identify themselves because their burns are so severe, police say.
An estimated 120sq m of replacement skin will be needed for all the patients, according to Dr Peter Watson from New Zealand's National Burns Unit.
Surgeons in burns units around the country are working around the clock, authorities say.
Some of the Australian victims have been flown back to their home country, and more are expected to follow in the coming days.
White Island is a popular tourist destination off the northern coast of North Island, and there were day tours and scenic flights available.
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