The White House rebuked the Republican former vice-president Mike Pence on Monday, for making jokes about US transportation secretary Pete Buttigieg, maternity leave and postpartum depression that it said were homophobic and offensive to women.

“He should apologise to women and LGBTQ+ people,” said Joe Biden’s press secretary, Karine Jean-Pierre.

Buttigieg is the first openly gay cabinet secretary confirmed by the US Senate.

He and his husband, Chasten Buttigieg, have twins. In October 2021, as the US faced supply chain problems and familiar issues with rail and air delays and safety, the two babies were hospitalised.

At the time, Pete Buttigie described “a terrifying few days” for the family.

He also responded to rightwing criticism and homophobic remarks from the Fox News host Tucker Carlson, calling criticism of his parenting and use of parental leave “strange”, from “a side of the aisle that used to claim the mantle of being pro-family”.

Pence, an evangelical Christian who was a congressman and governor of Indiana before becoming Donald Trump’s vice-president, is now considering a run for the Republican presidential nomination.

He spoke on Saturday at the Gridiron dinner, a bipartisan Washington event featuring light-hearted speeches. Phil Murphy, the governor of New Jersey, spoke for Democrats and the secretary of state, Antony Blinken, spoke for the Biden administration.

Pence made headlines for saying Donald Trump “endangered my family” on January 6 and rejecting attempts by right-wingers including Carlson to downplay the attack on Congress.

But when it came to his jokes, Pence took aim at Buttigieg.

Saying the secretary had taken “maternity leave” from his job, Pence added: “Thousands of travelers were stranded in airports, the air traffic system shut down, and airplanes nearly collided on our runways.

“Pete is the only person in human history to have a child and everyone else gets postpartum depression.”

The Associated Press said the remarks prompted criticism “even before the dinner was over”.

On Monday, Jean-Pierre said: “The former vice-president’s homophobic joke about Secretary Buttigieg was offensive and inappropriate, all the more so because he treated women suffering from postpartum depression as a punchline.

“He should apologise to women and LGBTQ+ people, who are entitled to be treated with dignity and respect.”

Pence’s former chief of staff dismissed the White House rebuke.

“The hypocrisy is especially rich considering their own secretary of state, Antony Blinken, joked that he yearned for ‘the old days’ when ‘Jews did all the work’,” Marc Short tweeted, referring to another remark at the dinner.

Chasten Buttigieg posted to Twitter a picture of his husband in hospital, holding one of the twins, and said he had “an honest question” for Pence.

“If your grandchild was born prematurely and placed on a ventilator at two months old – their tiny fingers wrapped around yours as the monitors beep in the background – where would you be?”

Pence did not immediately comment.

Before running for president and then joining Biden’s cabinet, Buttigieg was for eight years mayor of South Bend, Indiana. Pence was governor for four of those years and the two men worked well together.

But Pence also attracted widespread criticism for his views on LGBTQ+ rights. On the campaign trail in 2019, Buttigieg took aim at the older man.

“If me being gay was a choice, it was a choice that was made far, far above my pay grade,” Buttigieg said. “And that’s the thing I wish the Mike Pences of the world would understand: that if you’ve got a problem with who I am, your problem is not with me. Your quarrel, sir, is with my creator.”