"It is heartening to see the international community come to the aid of the people of Nepal. Our USAR team remains ready to assist if needed, and the Government will continue to assess how we can further contribute," Mr McCully said.
Labour's acting leader, Annette King, said Mr McCully should go back to Nepalese authorities to offer any possible assistance after it turned down the search and rescue assistance.
Ms King said it was unclear why New Zealand's offer of search and rescue team had now been turned down and it was possibly because it was left too late and other countries had already stepped in.
She said New Zealand had a lot of expertise in such situations following the Canterbury earthquakes and Mr McCully should go back to Nepal and ask what else it could contribute.
"I don't think he should just stop because there is some view we are not needed there. I think he should go back, offer humanitarian support. And of course I think $1 million is just a starting point."
Labour's foreign affairs spokesman David Shearer had urged New Zealand to send a team quickly as soon as the scale of the earthquake was clear on Saturday.
The USAR team was to have left Auckland for Singapore late last night, to then travel on to Kathmandu.
In announcing the deployment Mr McCully said Nepal had accepted the offer of a 37-strong contingent.
The personnel who were to go had expertise in rubble pile rescue, and included paramedics, a doctor, a structural engineer, logistics personnel and a Ministry of Foreign Affairs and Trade liaison officer.
Members of the group were involved in USAR efforts after the 2011 Christchurch earthquake.
Generators, rescue gear, batteries and food had been stored at the Auckland City Fire Station ahead of the planned deployment.
The team was to be deployed for up to 14 days initially and would have been fully self-sufficient while in Nepal.
New Zealand has pledged an initial $1 million contribution to the immediate relief effort.
-Claire Trevett contributed reporting
