Aid agencies are digging pit latrines in the camps on Saturday after an outbreak of diarrhoea.
Health authorities have also warned of malaria and cholera if sanitary conditions in the camps do not improve.
Large quantities of rice for the more than 2,000 survivors sheltering in primitive camps have been unloaded at Gizo harbour, which lost most of it wharves and jetties.
Nancy Jolo of the Red Cross in Gizo said: "Aid is arriving steadily now and we are getting it to the camps as quickly as we can."
Aid workers and officials have warned the death toll could rise sharply as reports come in from outlying islands and as bodies from the double disaster are formally identified.
There have been constant tremors since Monday's quake, with four aftershocks hitting the region on Friday night, one of them measuring five on the Richter scale.