Frontier Airlines' parent is planning to buy a stake in low-cost carrier WOW Air, the companies said Thursday, the same day Icelandair Group announced it had scrapped a planned acquisition of its ailing rival, calling WOW's fate into question.

Indigo Partners, a Phoenix-based private equity firm which owns Frontier, has invested in discount carriers in Latin America and Europe. Indigo said it has reached an in-principle agreement with WOW Air to invest in the Icelandic airline. The terms were not disclosed.

"We have a strategic vision for the airline, and look forward to working with its employees and agents to deliver that vision," said Bill Franke, managing partner of Indigo Partners in a news release.

Franke is a veteran of the low-cost airline world. The firm had once owned Spirit Airlines, and helped grow and shape the once-struggling carrier. In addition to Frontier, Indigo Partners has invested in Chile-based JetSmart, Mexico's Volaris Airlines and Hungary-based Wizz Air, all discount airlines.

Indigo Partners is also a major purchaser of Airbus jets. WOW operates an all-Airbus fleet.

The investment, if finalized, is a new twist in the fortunes of struggling WOW Air.

The Icelandic WOW Air said this week that it has faced escalating financial problems since its bond issuance in September, including higher fuel costs.

Aircraft lessors and the company's creditors have "demanded stricter payment terms than before, putting further pressure on the company's cash flow," WOW Air said in a statement Tuesday. The airline reduced its fleet by four planes earlier this week.

The low-cost carrier, which expanded rapidly and helped fuel a tourism boom to Iceland, has grappled with other problems as well, including complaints about poor customer service.

"We have to do better," WOW's Chief Executive Officer Skuli Mogensen told CNBC in an interview in June in Iceland's capital of Reykjavik. "It's obviously in our interest to fix it." He said problems such as canceled flights and delays have cost the airline in terms of lost passengers and the money paid out as compensation.

"This conclusion is certainly disappointing," Bogi Nils Bogason, Icelandair Group's interim president and CEO, said in a statement after the company scrapped plans to acquire its rival WOW Air. "We want to thank WOW Air's management for a good cooperation in the project during recent weeks. All our best wishes go out to the owners and staff of the WOW Air."

WOW Air's flights first took off in 2012 and it has expanded rapidly, adding trans-Atlantic service from several U.S. cities. The airline is a no-frills budget carrier, that offers low airfares, some below $100 one-way. It charges passengers for everything else, such as seat assignments, carry-on baggage and food and beverages.