The admiral emerged from the talks with Dr Coleman saying one of the reasons he was in New Zealand was to say thank you for the work of the SAS with the Afghan Crisis Response Unit.
"Your special forces operating in Kabul, Afghanistan, raised the level of capability of the Afghan security forces to a degree that they are now ready to take over their own security," Admiral Stavridis told reporters at Parliament.
"That was something New Zealand led the way on and did a terrific job."
The SAS deployment, the fourth since since 2001, ended 12 days ago in Kabul.
Admiral Stavridis visited the SAS base in Papakura on Tuesday.
Asked about where he saw the potential in New Zealand's future work with Nato, he cited Afghanistan, piracy and cyber.
"All of the threats we face today are transnational, they are global and so there is a role for all of us to work together to face them."
Admiral Stavridis said he was cautiously optimistic about the future in Afghanistan after 2014.
It was important to note that eight million boys and girls went to school there, 40 per cent of them girls; there were 16 million cellphones; that minerals were being developed and the economy was growing at 6 to 7 per cent a year.
Nato and coalition troops would be significantly downsized after 2014 as security was turned over to Afghan troopers and there would be a small training and mentoring presence.
Commenting on the first bilateral combat-focused exercise between the United States and New Zealand in the central North Island this month, Admiral Stavridis said the United States was putting a great deal of focus on the Pacific region.
"We like to think of the United States as a Pacific nation. We are looking forward to continuing those strong relationships that we have here with New Zealand, with Australia and with other allies in the Pacific. The future is bright for New Zealand-US co-operation."
Asked if a US ship was likely to visit, the admiral said: "I don't have any visibility into that at this point."
Dr Coleman added: "It's not on the agenda for us at this point."