"Whether that can happen under the proposed changes to the constitution we have yet to know," Mr McKinnon said.
"It will take a few days for the air to be cleared before we have any idea which political direction this interim Government is going to take. Our obvious plea is: the sooner you can return to democratic rule the better."
Mr McKinnon said he had seen a draft list of the proposed cabinet of new President Ratu Josefa Iloilo.
"Some of them I know, some I have heard of, but you are seeing very strong Fiji nationalistic feelings emerge in this."
Mr McKinnon said while it was a relief to see the hostages released, the future of Fiji Indians looked dim.
However, he said coup leader George Speight and his fellow nationalists did not understand what could happen to Fiji if it shunned the wishes of the Commonwealth.
"A lot of Fiji's income comes from very heavily subsidised prices for their sugar. If that money doesn't come into Fiji, where is its money going to come from? If tourism falls off in Fiji where is the money going to come from?
"Fiji rugby players want to play for Fiji but if Fiji can't play with anyone, what are they going to do? Fiji could be excluded from a lot of things in the near future."
The country had to keep working within the 1997 constitution to stay onside with the Commonwealth.
"If that '97 constitution is changed to such a degree where people of Indian origin are just being totally marginalised, then the Commonwealth view on that will be very serious."
Mr McKinnon said now that the hostages had been released he expected Fijian Indians to become more vocal.
As well as the Fiji coup, the problems in the Solomons, the intense concern about the elections in Zimbabwe and the ongoing tensions in Sierra Leone had kept Mr McKinnon's office busy.
He has had to deal with the issues as they have developed by the day and his experience and contacts as New Zealand's former foreign minister have been invaluable.
He never had a chance to limber up and find his feet when he arrived at his big office in Marlborough House in central London. With a staff of 300, he still needs to know how the office runs.
But in his own cheerful Kiwi style, he has got around his staff and broken down the former starchy hierarchy in a concerted bid to foster a team effort.
"We have some of the finest minds in the world here, but I've got to confess I don't know exactly what they all do.
If we come to a lull period with fewer conflicts, I'll get a better feel for the place.
"For me, the pressure of being foreign minister in Wellington was more intense, dealing with so many issues. There was always one New Zealander a week getting into an awful amount of trouble. The job was made a lot easier when I dropped off being deputy prime minister in 1997.
"Here work is more steady, but the big issues are just that."
Mr McKinnon has given New Zealand domestic issues a wide berth, especially political matters relating to sacked Maori Affairs Minister Dover Samuels and former Oceania soccer chief Charlie Dempsey.
As well as the working side of the job, he is also having to work around the demands of being a member of London's high society.
"The British have a strong hierarchal sense and the Commonwealth Secretary-General sits pretty high. If you don't go to a dinner there's a very obvious gap usually right up at the top table.
"An amazing function was held last week for Australia Week at the Guildhall where there were five former Australian prime ministers, three former British prime ministers, my next-door neighbour [Prince Charles] and others.
"So there is a big role in this job. You are the face of the Commonwealth Secretariat, which means you are expected to be out there and making yourself known and meeting people."
- NZPA
More Fiji coup coverage
Main players in the Fiji coup
The hostages
Under seige: map of the Parliament complex
Fiji facts and figures
Images of the coup - a daily record
George Speight: "I’m certainly not mad."
