Pete Buttigieg, the U.S. transportation secretary, said on Tuesday that he and his husband, Chasten, were completing the process of becoming parents.

“The process isn’t done yet and we’re thankful for the love, support, and respect for our privacy that has been offered to us,” Mr. Buttigieg, the first openly gay cabinet member confirmed by the Senate, wrote on Twitter. “We can’t wait to share more soon.”

The Buttigieges, who did not respond to phone calls and messages seeking more details about the announcement, had been exploring adoption in recent months.

Mr. Buttigieg, 39, wed Chasten, 32, in 2018, about 10 months before starting his presidential campaign. As Mr. Buttigieg's national profile grew, he and Chasten, a former middle school teacher, have often worked to challenge perceptions of gay relationships.

“People are accustomed to politics looking a different way, and you’re here to make sure that, you know, it can look a different way,” Chasten said in an interview with The Times this spring.

In February 2020, Mr. Buttigieg, who is recognized inside the administration for his deftness as a public speaker, hit back at the radio host Rush Limbaugh, who questioned his ability to hold his own on the debate stage with former President Donald J. Trump.

“How is this going to look?” Mr. Limbaugh said on his show at the time. “A 37-year-old gay guy kissing his husband onstage next to Mr. Man Donald Trump?”

Mr. Buttigieg’s answer challenged the idea that Mr. Limbaugh should be considered an arbiter of masculinity: “Look, I guess he just has a different idea of what makes a man than I do,” Mr. Buttigieg said during an interview on Ellen DeGeneres’s talk show. “Look, I’m not going to take lectures on family values from the likes of Rush Limbaugh or anybody who supports Donald Trump, frankly.”

On Tuesday, activists said that the couple’s announcement had the potential to similarly reframe assumptions of gay fatherhood.

“As parents, they will now shine a national spotlight on L.G.B.T.Q. families, who often face daunting challenges because of outdated policies that narrowly define what families are,” Annise Parker, the president of the Victory Institute, an organization that helps prepare L.G.B.T.Q. people to run for political office, said in a statement.