The company would not buy shares at a price more than 5 per cent above the five-day volume-weighted average market share price, as required by ASX rules.
Air New Zealand's share price increased 6c yesterday to close at $1.16.
Fyfe said the past financial year saw a marked improvement in performance compared with the previous year but the airline still had some way to go before it delivered the level of returns shareholders should expect.
The airline remained committed to its core strategy of investing in the business and continued to innovate and adapt to a changing market and competitive conditions. "As a result we are now well positioned to deliver improved performance, even at these elevated fuel prices and despite many airlines projecting further deterioration in their performance."
However, the airline faced increased competition from Jetstar, which is adding another aircraft to its main trunk domestic route, and would feel some impact from the proposed Qantas-Emirates partnership.
In response to a question Fyfe said Emirates was a "very effective competitor" and was expanding its network globally.
While there would be no material impact on Air New Zealand's Tasman operations, there could be more competition on long-haul routes.
"Qantas and Emirates joining up forces ... will have an impact on us," Fyfe said.
"We could see a return at some point of Qantas or a combination of the two airlines on the Auckland-Los Angeles route and further competition from the two airlines up to Europe," he said.
"We're confident we can continue to adapt our business to that threat and we're sure we'll see further competitors come and go from the market in our future."
He said the delay of the delivery of fuel-efficient 787 Dreamliners - likely to end up being four years - was frustrating and had impacted the bottom line, even though it had received compensation from Boeing.
"We remain confident that when these aircraft enter into service in 2014 they will be a game changer and the payoffs will be tangible."
Chairman John Palmer is also into his last term in the role and he paid tribute to Fyfe, who he said started in the top job with having to restructure the engineering business.
"That process set the tone of his leadership - well reasoned and researched initiatives, well communicated ideas and vision, determination to improve outcomes, and above all ... trusting and encouraging people to go above and beyond in their daily activities."
Palmer said Air New Zealand was the only airline in Australasia to have consistently paid a dividend during the past seven years.
"This is a reflection of our high- performing management team, who have been able to achieve consistent profitability through one of the toughest periods the airline industry has ever experienced."
Fyfe leaves the company at the end of the year and will be succeeded by Christopher Luxon, who has been the airline's long-haul boss.
