World Vision says there have been more than 150 aftershocks in Solomon Islands since a magnitude 8.0 earthquake and tsunami on Wednesday.
A magnitude 6.3 earthquake centred 51km south-west of Lata at a depth of 35km occurred on Monday morning.
The ABC reports it followed a magnitude 6.5 quake early Sunday which was centred 29km south-southwest of Lata at a depth of 18km, and a 7.0 aftershock late on Friday night.
World Vision director Andrew Catford said the aftershocks frighten people into heading for higher ground in case there is another tsunami and some were killed by falling debris.
He said the number of dead is now 11.
The aftershocks have also caused liquefaction and made the wharf in Lata drop, hampering aid deliveries.
However, food, shelter kits and a water purifying machine have now arrived in the Santa Cruz Islands.
The Red Cross says the only form of contact is by mobile phone.
Secretary general Joanne Zoleveke said email services are down and no official assessment reports have been received.
Supplies en route from NZ
Six tonnes of goods donated by the Warehouse and ShelterBox left Whenuapai air base on an RNZAF plane on Monday morning.
World Vision chief executive Chris Clarke said most of the supplies will be going to Temotu, the area which bore the brunt of the magnitude eight earthquake.
He said the Boeing 757 is on a pre-arranged diplomatic tour of the Pacific and is expected in Honiara on Thursday.
Tents, blankets, towels and tarpaulins are on board, as well as hand-sanitizer, soap and candles.