US private equity firm Indigo Partners has withdrawn its offer to buy a stake in Iceland's loss-making carrier WOW Air, and Icelandair is now back in talks to buy the no-frills airline, the carriers said.

Icelandair had previously agreed to buy WOW Air but ditched those plans on November 29.

A day later, Indigo Partners, a private equity group that owns stakes in several low-cost airlines including Frontier Airlines in the United States, said it had reached a preliminary deal to acquire 49 percent of WOW Air.

"The proposed investment of Indigo Partners in WOW Air has been cancelled by Indigo Partners... Subsequently WOW Air has started discussions with Icelandair Group," WOW said in a statement issued late Thursday.

WOW Air, founded in 2011, exploited Iceland's location in the middle of the North Atlantic to offer a low-cost service between Europe and North America as well as tapping into a tourist boom to the volcanic island.

However, the privately-owned airline posted a pre-tax loss of almost $42 million for the first nine months of 2018.

Indigo's planned investment of $75 million was recently raised to $90 million, suggesting there were gaping holes in WOW's finances and more debt than previously thought.

The collapsed talks are the latest setback for WOW Air, after months of searching for an investor.

Icelandair said the discussions would be "based on the doctrine of competition law regarding the failing firm defence", which means that buyers try to convince regulators that a deal wouldn't have a considerable impact on market competition as the purchased firm would likely go out of business if there was no deal.

Icelandair added that "the discussions will take place in cooperation with the Icelandic authorities."

The Icelandic government said in a statement that authorities were "supportive of these discussions and are willing and prepared to use all reasonable efforts to facilitate a positive outcome."

WOW Air has undergone major restructuring in a bid to ensure its survival, reducing its fleet from 20 to 11 aircraft, eliminating several destinations, including those to the United States, and cutting 111 full-time jobs.

WOW Air transports more than a third of those travelling to Iceland, and plays a large role in the country's important tourism sector.

A report by a governmental work group said a WOW Air bankruptcy would lead to a drop in Iceland's gross domestic product, a drop in the value of the krona and rising inflation.

WOW Air and Icelandair said they hoped to conclude their negotiations by March 25.