Officials from the White House, the State Department, Defence, Commerce, USAid, the Coast Guard and the Peace Corps make up the delegation of 50, the largest any country has fielded.
Asked about China's influence in the region, Mr Nides said: "We look at our relationship with China in the same way as we look at it around the world.
"We are partners, we work together and are very comfortable with our relationship.
"We are all here for the same objective: to show our support for the Pacific Islands."
Mr Nides said President Barack Obama was focused on what the US was doing in the region and "more importantly showing our deep and ever-lasting friendship with those in New Zealand".
Mr Cui took part in an inaugural Pacific consultations between China and the US in June this year in Hawaii, with US Assistant Secretary of State for Asia Pacific Kurt Campbell, who is also part of the US delegation to New Zealand.
McCully welcomed the US presence and said: "We also think the re-engagement in the Asia part of the Asia Pacific region through the East Asia summit is something that is of great benefit to our wider region as well."
Meanwhile, the US has confirmed it will establish a USAid base in the Pacific - but in Papua New Guinea, not Fiji as announced last year by Secretary of State Hillary Clinton.
Nisha Biswal of USAid said the US already funded an HIV programme in PNG, but it is believed New Zealand and Australia lobbied against basing the programme in Fiji.