But a reciprocal visit from a US Coastguard vessel - an idea first proposed by Prime Minister John Key - will not happen anytime soon.
"That's something that is entirely in their hands," Mr McCully said.
"They obviously decide what to do with their own vessels, and if they were to indicate they wanted to do something of that sort, we'd obviously go through the normal processes."
Mr McCully said New Zealand remained suspended from the Anzus alliance and continued to have an independent foreign policy, but the it was trying to have "the best possible relationship with the US".
He said the Government remained committed to its anti-nuclear policy.
"I think it's something that we're known for, and the Government that I'm a part of made it clear that we wouldn't change it, that we would regard it as an important part of our legacy."
Mr McCully said he did not see New Zealand's growing relationships with both the US and China - two of the major players in the Pacific - as a problem.
"I see it as an opportunity, and indeed that was reinforced in my conversations with the United States officials last week. They're looking at China and trying to work out how they're going to engage more positively with China and other parts of Asia as well."
Mr McCully said New Zealand needed to be thoughtful and strategic, and would deal with issues on their merit - which was what New Zealand was known for.
He said New Zealand's bid for a place on the United Nations Security Council would put the country in a high-profile position, but the issues it dealt with would remain the same.
"I think the Security Council is something that we will do very well on. I'm confident that we've got a good shot at this, and it's very important that when you run only every 20 years or so that you are able to succeed."
Mr McCully said he was "absolutely not" interested in the UN as a career after politics.
"I've heard that rumour before. I can absolutely rule that out."