New Zealand has had a formal claim on the region since 1923. The Government does not have legal power to ban nuclear-powered ships from the Ross Sea, but has a strict anti-nuclear policy in the dependency.
Mr McCully was alerted to the US proposal by Ministry of Foreign Affairs and Trade (Mfat) officials.
On his orders, Mfat negotiated for several weeks and persuaded the foundation to use a non-nuclear ship.
Mr McCully told the Herald that a nuclear-powered ship in the dependency would have been "extremely unhelpful" to political relations.
"I think it's pretty clear that this would have been a sensitive issue for New Zealand and I'm delighted that the US ... was able to find an alternative approach.
"It would have been very unhelpful to have a nuclear-powered vessel involved. New Zealand enjoys a very constructive and co-operative relationship with the US in terms of our logistics pool."
The Government was particularly worried about the timing, with the US close to signing a contract for the Russian ship in the run-up to the general election in November.
The prospect of New Zealand supply ships depending on a nuclear-powered icebreaker heightened the Government's embarrassment.
One New Zealand official said that, as countries jostled for position at the mineral-rich continent, New Zealand would come under increasing pressure to rethink its anti-nuclear policy in the Ross Sea.
Mr McCully said he was unsure if the US or other nations would attempt to use a nuclear-powered ship for Antarctic trips in the future.
Russia had the largest fleet of icebreakers in the world - seven of them nuclear-powered - and was believed to be seeking a closer relationship with New Zealand on Antarctic projects.
The US has a small, ageing fleet of icebreakers and its Antarctic programme has depended on a Swedish ship, Oden, since 2006. But that ship was unavailable last year and the foundation ended up securing the 30-year-old diesel-powered Russian icebreaker Vladimir Ignatyuk.
The sophisticated icebreakers cost up to $1.2 billion to build and hundreds of millions to upgrade.
The floating port at McMurdo Sound was blocked by 10km of ice and an icebreaker took around two weeks to cut through it. The US container ship and tanker which travelled through the channel provided supplies to the largest community in Antarctica, McMurdo Station.
The Weekend Herald understands there was concern about the nuclear-powered icebreaker's potential voyage across the equator. Icebreakers are designed for cold weather operations, and a passage through tropical waters could complicate the cooling system for its nuclear technology.
