The Indian army says planes have dropped food and water to tsunami survivors on all the inhabited islands in the Andaman and Nicobar chain.
Relief supplies have begun arriving in Port Blair
There was criticism that aid has been slow to reach survivors, thousands of whom may be sheltering on high ground.
Outbreaks of disease have been reported on remote southern islands and doctors have been rushed there, officials said.
More than 9,000 people are known to have died in India, 812 of them on the islands, with thousands more missing.
More than 50 people in the devastated Lakhsmi Nagar area close to Campbell Bay in the Nicobars are now suffering from the potentially fatal diseases of malaria or diarrhoea, the islands' chief administrator Ram Kapse said on Sunday.
He said medical teams were being deployed in affected areas, but the BBC's Subir Bhaumik in the capital, Port Blair, says Mr Kapse has so far denied permission for international agencies to send their own staff.
Our correspondent adds that aid workers have been worried about possible outbreaks of water-borne diseases because the tsunami polluted wells and other sources of drinking water.
Earlier on Sunday, the military commander in charge of the relief effort said the most remote locations had now been reached.
"This is the biggest relief effort in the history of India," home ministry junior minister Sri Prakash Jaiswal said from Port Blair, the Associated Press news agency reported.
ANDAMAN AND NICOBAR
About 400 islands, 38 inhabited
Islands are peaks of submerged mountain range
Indian territory, area of 8,249 sq km
Population around 370,000, about 100,000 in Port Blair
Number of tribes, including Jarawas, Onges and Shompens
"We are reaching everywhere with aid. I still have hopes that there will be survivors among the missing people," he added.
More than 3,000 people were evacuated to the mainland and relief camps in the capital on Friday.
They said the situation was desperate in some areas.
"There is nothing to eat there. There is no water. In a couple of days, people will start dying of hunger," said Anup Ghatak, an evacuee from Campbell Bay on the southern tip of the chain, quoted by AP news agency.
Relief efforts in the archipelago's 38 inhabited islands have been hampered by the destruction of most of the islands' jetties.
The island chain, close to the epicentre of last Sunday's earthquake, has also felt a number of aftershocks.
More than 5,400 people are still thought to be missing on the islands, but the local police chief has said he believes most of the missing are probably dead.
Some, including many tribal people in remote areas, may be alive in jungles.
In Tamil Nadu - the worst hit state on the Indian mainland - the arrival of bodies at main hospitals has begun to slow down.
Many refugees are now looking forward, saying they want to get back to a more normal life, a week after the waves smashed into the coast, destroying lives and livelihoods.
Initial aid packages of rice, kerosene, cooking utensils and some money are being distributed, though the BBC's Sampath Kumar reports that some fishermen say they would rather have nets and boats so they could begin to take care of themselves.
A naval vessel docked at Nagapattinam bringing doctors, nurses and large amounts of medicine to the devastated area.
The state's Chief Minister Jayalalitha says free textbooks and uniforms will be distributed to affected children.
The government also announced that the children of the dead would be adopted by the state and orphanages for up to 100 children would be set up in three towns.