"The main hospital in Honiara is stretched after the recent flooding and there is a very serious risk of waterborne disease spreading around the capital,'' he said.
New Zealand would also ship a Bailey bridge to Honiara to maintain a link between the airport and the city centre.
"The Mataniko Bridge was damaged in the initial flooding and the Bailey bridge from the New Zealand Transport Agency will help ensure transport links are maintained while it is repaired,'' Mr McCully said.
At least 21 people have been killed by the flooding. No major damage was caused by the earthquakes.
For more on the recent natural disasters to hit the Solomons, go here.
Mr McCully said the Solomon Islands Government had asked for help to assist with the "exhausted resources they have within their health system to deal with people who are caught up, particularly in the evacuation centres".
Details were still being finalised, but Mr McCully said New Zealand was looking to send two teams of 10 staff.
The Solomons had also requested transport infrastructure aid, and New Zealand was considering whether to help with temporary truss bridges.
World Vision's humanitarian and emergencies manager in the Solomons, Dwain Hindriksen, said the agency had several New Zealanders in the area providing aid.
The earthquake had been widely felt, but did not appear to have caused significant damage.
"We were sitting down, having a meeting. There were a few tables shaking and struts in the roof were moving.
"But I haven't heard of any damage - which is good, considering what the population has gone through with the flooding."
World Vision's role would continue to be flood-related, he said.
"The water is starting to dry up, but the affects of the flooding is still there and will be for some time."
Yesterday's quake came just over a week after heavy rain led to flash floods in Honiara, when the Mataniko River burst its banks, destroying homes and killing up to 21 people. Many more are still missing.
Up to 50,000 people have been affected and the wiping out of sewerage systems has resulted in a rush from help agencies working to prevent disease.
Red Cross NZ communications manager Corinne Ambler was in the Solomons for a week. She arrived back in New Zealand a day before the earthquake struck.
Ms Ambler said the situation was overwhelming, but people remained resilient.
"I went up the river in Honiara and it's just devastating.
"Homes have been tossed around like matchsticks and everything is buried in mud - it's like that all up the river."
She said she had visited one home where a grandfather died with three of his grandchildren.
Many people were doing their best to help others, despite having lost everything themselves.
"Some of the volunteers who come and help every day have lost their own homes, yet they continue to volunteer.
"So much has happened there. But the Solomon Islands people, I found them to be really resilient and very warm. They're just getting on with things."
How to help
Save The Children: 0800 167 168 or www.savethechildren.org.nz
Unicef: 0800 243 575 or www.unicef.org.nz
Oxfam: 0800 600 700 or www.oxfam.org.nz
World Vision: 0800 800 776 or www.worldvision.org.nz
Red Cross: 0800 RED CROSS or www.redcross.org.nz
