NEW YORK — United Continental is facing an insurrection among its shareholders, led by the well-regarded former chief executive of Continental Airlines, Gordon M. Bethune.

Bethune is one of six director candidates put forward on Tuesday by two hedge funds, Altimeter Capital Management and PAR Capital Management, which together own about 7.1 percent of United’s shares.

The decision by the activist hedge funds to raise a public challenge to the airline’s board comes after United’s announcement on Monday to add four independent directors.

The contest comes at an awkward time for United, which appointed a new chief executive in September after the surprise dismissal of Jeff Smisek during a corruption investigation involving officials at the Port Authority of New York and New Jersey. It also comes just days after the airline said that the new chief executive, Oscar Munoz, would return to work full time on March 14, after undergoing heart transplant surgery in January.

In a statement, Altimeter and PAR said that they chose to begin their proxy fight after weeks of discussions with United’s board. The hedge funds also described the airline’s board expansion as “a knee-jerk response to the stockholders’ efforts.’’

The activists argue that United has badly underperformed over the last five years, despite its name recognition and size, which the hedge funds argue arises from its board.

“We have no more confidence that you will act responsibly in the future (even with yesterday’s announcement) than we have evidence that you have done so in the past,’’ Brad Gerstner, the chief executive of Altimeter, and Paul A. Reeder, the chief executive of PAR, wrote in a public letter to United’s board.

Henry L. Meyer III, the airline’s nonexecutive chairman, ­replied in a statement, “We are deeply disappointed that after United attempted to engage in a constructive, good-faith dialogue with PAR and Altimeter, repeatedly communicated our willingness to make meaningful changes in our board, publicly ­announced our intention to name four new independent ­directors with deep relevant ­experience, and named three of them yesterday, PAR and Altimeter have unilaterally taken this hostile action with no concern that a proxy fight could distract the company from executing on Oscar’s strategic plan.’’

In an interview, Bethune said he had agreed to join the slate to become nonexecutive chairman for two years to help the board set clear goals and motivate employees. He said that before United’s latest nominations, the company’s board lacked directors with experience running an airline.

Bethune, who is serving on the boards of three companies — Honeywell, Prudential, and Sprint — plans to retire from two this year but will remain on the board of Sprint. When he ran Continental, he appointed both Munoz and Meyer, the current chairman of United, to the airline’s board.

“I don’t need this,’’ he said, and added that United employees were demoralized and he wanted to help.

“There is nothing wrong with the people. They just need leadership. And they don’t have it,’’ he said.