It asks about their availability over the next one to four months to deploy "to a country that may have a Covid-19 outbreak or Covid cases in the community" for up to eight weeks at a time.
Fiji is the only country in the NZmat zone with a community outbreak.
The email said people would have to prove they were fully vaccinated to be able to go.
A Ministry of Foreign Affairs spokeswoman said sending more medical personnel was a possibility but no decision had been made yet.
It continued to work closely with the Fiji Government to determine if more support was needed, she said.
Christchurch anaesthetist Wayne Morriss is one of the two NZ doctors in Fiji now.
He told Morning Report doctors and nurses there were working incredibly hard, often seven days a week.
New Zealand and Australian medical teams have been helping Fiji to improve its systems so hospitals can manage severely ill Covid-19 patients, as well as people who need urgent surgery, like emergency caesareans.
In the past 24 hours some less sick Covid-19 patients were moved from the hospital to the national gymnasium in Suva, where they could be monitored but transferred back to the hospital if needed, he said.
There were also clinics at a sports arena and tents outside of it.
Getting the whole country vaccinated was critical, and it was going very well so far, with about 55 per cent of people having their first dose of the AstraZeneca vaccine, Morriss said.
- RNZ
