Ms Clements said there were concerns around maternal health, with pregnant women and women who have recently given birth without shelter, power and water.
Meanwhile, the Vanuatu government has taken control of all aid distribution and coordination.
"The government is doing absolutely everything it can to get the response working in the right way," Ms Clements said.
Unicef is assisting the Ministry of Health in Vanuatu with a measles vaccination campaign as part of its approach the health assistance.
Vanuatu was in the midst of a measles outbreak before cyclone Pam tore through on Friday, and the rate of immunisation in the country is about 33 per cent.
Six teams of health workers are working to target vaccination of children in at-risk communities and evacuation centres where measles had been confirmed.
Up to six additional teams are expected to be trained to start by the end of this week, focusing on an integrated health response, including vaccination, vitamin A distribution and bed net distribution for protection against malaria.
Unicef is also distributing health supplies for children and families including basic health kits, oral rehydration salt sachets, zinc tablets, vitamin A capsules, and de-worming tablets.
After two failed flights yesterday, Foreign Minister Murray McCully said a New Zealand Defence Force (NZDF) C-130 Hercules aircraft has travelled to Tanna Island, Vanuatu, this afternoon with relief supplies.
Tanna Island is about 230km south of Port Vila and early aerial surveillance showed widespread destruction of houses and buildings.
"Getting relief supplies to the outer islands is an urgent task," Mr McCully said.
"On board this flight were NZDF personnel, a Red Cross team, and almost seven tonnes of relief supplies, including tarpaulins, 100 toolkits, six chainsaw packs, and four generators."
The aircraft also transported Vanuatu Prime Minister Joe Natuman to allow him to assess the damage firsthand.
"The New Zealand government is currently considering further options to assist the people and government of Vanuatu to recover from this catastrophic cyclone," Mr McCully said.
To date, the New Zealand government has contributed $2.5 million dollars and made a number of Defence Force aid flights.
Red Cross communications aid worker Hanna Butler, who was on a flight over Tanna today, said what was usually a lush tropical island now looked "barren and brown".
"Trees have been stripped of their leaves and most of the houses which are still standing have lost their roofs. Those that were not built with concrete have almost all disappeared, as if they had never existed."
New Zealanders have donated around $280,000 to the Red Cross Tropical Cyclone Pam appeal fund so far.
From today, Countdown customers can donate to the Oxfam New Zealand Cyclone Pam Appeal for Vanuatu at any Countdown store across the country at donation boxes or through the Eftpos terminal.
