NEW YORK — Before he died in a wingsuit accident in Switzerland three years ago, daredevil Donald Zarda filed a lawsuit claiming he had been sacked from a skydiving instruction job after telling a client he was gay.
Now, a federal appeals court in New York is trying to decide whether US antidiscrimination law protects employees from being fired due to sexual orientation.
One US government agency, the Equal Employment Opportunity Commission, says it does. Another, the Department of Justice, says it doesn’t.
The rare face-off between two executive branch entities played out Tuesday before an equally rare assembly of 13 judges of the Second US Circuit Court of Appeals.
For about two hours, the judges peppered the lawyers with questions about Title VII of the 1964 Civil Rights Act, which bars employment discrimination on the basis of ‘‘race, color, religion, sex or national origin.’’
Most federal appeals courts in the past have ruled that ‘‘sex’’ means biological gender, not sexual orientation. But a federal appeals court in Chicago ruled earlier this year that sexual orientation was also covered by the law.
The case was brought after Zarda was fired in 2010 from a skydiving job in Central Islip, N.Y., that required him to strap himself tightly to clients so they could jump in tandem from an airplane.
In an attempt to put one female student at ease about the physical contact, he told her not to worry; he was gay.
‘‘He was proud of being gay and in the male workplace of the skydiving community. Jokes were often made that loosened the tension of the experience and jokes were often sexual,’’ said attorney Greg Antollino, an attorney for Zarda’s estate.
The school fired Zarda after the woman’s boyfriend called to complain about his behavior.
Zarda’s lawsuit was initially rejected by a federal judge in Central Islip. A three-judge appeals court panel upheld the lower-court ruling in April, citing a 2000 Second Circuit ruling that concluded Title VII of the act does not cover sexual orientation.
The full Second US Circuit Court of Appeals then took the rare step of agreeing to rehear the case as a group, a step it usually takes less than once a year.
During arguments set for Tuesday, the Equal Employment Opportunity Commission and Justice Department will argue opposite sides of the issue.
‘‘You know we love to hear from the federal government, but it’s a little awkward for us to have the federal government on both sides of this case,’’ Circuit Judge Rosemary S. Pooler said.
A deputy assistant attorney general with the Justice Department, Hashim M. Mooppan, said the language of Title VII makes it clear that it does not cover sexual orientation.
Circuit Judge Denny Chin questioned whether court rulings made on the issue over the last half century should be revaluated.
‘‘The landscape changes in terms of the law, right? Marriage is different now,’’ Chin said. ‘‘Why can’t the same be said about sexual orientation?’’
Mooppan said Congress has the authority and could alter the law to include sexual orientation if it chose to make the change. At one point, he noted the wide latitude employers have to control the sexual behavior of their employees.
‘‘They’re allowed to say if you cheat on your spouse, you’re fired. They’re allowed to say if you’re promiscuous, you’re fired. None of that is covered by Title VII,’’ he said.
One judge suggested that the Justice Department changed its position after President Donald Trump was elected. The department filed its brief in the case on the same day Trump announced on Twitter that transgender people could no longer serve in the military.
A seemingly unflappable Mooppan grew uncomfortable only when the judge pressed to learn more about how the rift between the EEOC and Justice developed.
‘‘Can the EEOC file its own brief without consultation with Justice?’’ one judge asked.
‘‘Does DOJ sign off on a brief EEOC plans to file?’’ asked another.
‘‘I don’t think it’s appropriate for me to comment,’’ Mooppan said, adding at one point that answering the questions makes him nervous.
Zarda was 44 when he died.
Bill Moore, a longtime partner of Zarda who is pursuing the lawsuit along with Zarda’s sister, said in a telephone interview from his Dallas home that Zarda ‘‘would be shocked’’ that the lawsuit had gone so far since he was seeking something ‘‘very small’’ to compensate him for lost wages.
‘‘Don always felt like he didn’t really have very much of a purpose and so he wondered what that was,’’ Moore said. ‘‘He would be very happy to see where it is.’’
A ruling is not expected for some time.