WASHINGTON — The Supreme Court announced on Monday that it would decide whether the Civil Rights Act of 1964 guarantees protections from workplace discrimination to gay and transgender people in three cases expected to provide the first indication of how the court’s new conservative majority will approach L.G.B.T. rights.

The Equal Employment Opportunity Commission has said the 1964 act does guarantee the protections. But the Trump administration has taken the opposite position, saying that the landmark legislation that outlawed discrimination based on race, religion, national origin and, notably, sex, cannot fairly be read to apply to discrimination based on sexual orientation or transgender status.

The three cases the court accepted are the first concerning L.G.B.T. rights since the retirement last summer of Justice Anthony M. Kennedy, a champion of gay rights. His replacement by the more conservative Justice Brett M. Kavanaugh could shift the court’s approach to cases concerning gay men, lesbians and transgender people.

Most federal appeals courts have interpreted Title VII of the Civil Rights Act to exclude sexual orientation discrimination. But two of them, in New York and Chicago, recently issued decisions ruling that discrimination against gay men and lesbians is a form of sex discrimination.

The Supreme Court agreed to hear the case from New York, Altitude Express Inc. v. Zarda, No. 17-1623, along with one from Georgia that came to the opposite conclusion, Bostock v. Clayton County, Ga., No. 17-1618.

The New York case was brought by a skydiving instructor, Donald Zarda, who said he was fired because he was gay. His dismissal followed a complaint from a female customer who had voiced concerns about being tightly strapped to Mr. Zarda during a tandem dive. Mr. Zarda, hoping to reassure the customer, told her that he was “100 percent gay.”

Mr. Zarda sued under Title VII and lost the initial rounds. He died in a 2014 skydiving accident, and his estate pursued his case.

Last year, a divided 13-judge panel of the United States Court of Appeals for the Second Circuit allowed the lawsuit to proceed. Writing for the majority, Chief Judge Robert A. Katzmann concluded that “sexual orientation discrimination is motivated, at least in part, by sex and is thus a subset of sex discrimination.”

In dissent, Judge Gerard E. Lynch wrote that the words of Title VII did not support the majority’s interpretation.

“Speaking solely as a citizen,” he wrote, “I would be delighted to awake one morning and learn that Congress had just passed legislation adding sexual orientation to the list of grounds of employment discrimination prohibited under Title VII of the Civil Rights Act of 1964. I am confident that one day — and I hope that day comes soon — I will have that pleasure.”

“I would be equally pleased to awake to learn that Congress had secretly passed such legislation more than a half-century ago — until I actually woke up and realized that I must have been still asleep and dreaming,” Judge Lynch wrote. “Because we all know that Congress did no such thing.”

The arguments in the Second Circuit had a curious feature: Lawyers for the federal government appeared on both sides. One lawyer, representing the E.E.O.C., said Title VII barred discrimination against gay people. Another, representing the Trump administration, took the contrary view.

The Georgia case was brought by a child welfare services coordinator who said he was fired for being gay. The 11th Circuit, in Atlanta, ruled against him in a short, unsigned opinion that cited a 1979 decision that had ruled that “discharge for homosexuality is not prohibited by Title VII.”

The justices also agreed to decide the separate question of whether Title VII bars discrimination against transgender people. The case, R.G. & G.R. Harris Funeral Homes v. Equal Employment Opportunity Commission, No. 18-107, concerns Aimee Stephens, who was fired from a Michigan funeral home after she announced in 2013 that she was a transgender woman and would start working in women’s clothing.

“What I must tell you is very difficult for me and is taking all the courage I can muster,” she wrote to her colleagues. “I have felt imprisoned in a body that does not match my mind, and this has caused me great despair and loneliness.”

Ms. Stephens had worked at the funeral home for six years. Her colleagues testified that she was able and compassionate.

Two weeks after receiving the letter, the home’s owner, Thomas Rost, fired Ms. Stephens. Asked for the “specific reason that you terminated Stephens,” Mr. Rost said: “Well, because he was no longer going to represent himself as a man. He wanted to dress as a woman.”

The United States Court of Appeals for the Sixth Circuit, in Cincinnati, ruled for Ms. Stephens. Discrimination against transgender people, the court said, was barred by Title VII.

“It is analytically impossible to fire an employee based on that employee’s status as a transgender person without being motivated, at least in part, by the employee’s sex,” the court said, adding, “Discrimination ‘because of sex’ inherently includes discrimination against employees because of a change in their sex.”

John J. Bursch, a lawyer with Alliance Defending Freedom, which represents the funeral home, said the appeals court had impermissibly revised the federal law.

“Neither government agencies nor the courts have authority to rewrite federal law by replacing ‘sex’ with ‘gender identity’ — a change with widespread consequences for everyone,” Mr. Bursch said in a statement. “The funeral home wants to serve families mourning the loss of a loved one, but the E.E.O.C. has elevated its political goals above the interests of the grieving people that the funeral home serves.”

James D. Esseks, a lawyer with the American Civil Liberties Union, which represents Ms. Stephens and Mr. Zarda’s estate, said the cases concern elementary principles of fairness.

“Most of America would be shocked if the Supreme Court said it was legal to fire Aimee because she’s transgender or Don because he is gay,” Mr. Esseks said in a statement. “Such a ruling would be disastrous, relegating L.G.B.T.Q. people around the country to a second-class citizen status.”