Pete Buttigieg jabbed at Donald Trump during a Fox News town hall on Sunday, saying he understands why people and the media are “mesmerized” by the president’s tweets because “it is the nature of grotesque things that you can’t look away”.

Asked how he responds to Trump’s tweets and name-calling – including referring to Buttigieg as Alfred E Neuman, the Mad magazine character – the 37-year-old mayor of South Bend, Indiana, responded: “I don’t care.”

He said Democrats need to talk less about Trump and more about what they’ll do for the American people.

Trump criticized Fox News earlier Sunday for “wasting airtime” on Buttigieg, saying Fox “is moving more and more to the losing (wrong) side in covering the Dems”. He added, “Alfred E Newman [sic] will never be president.”

Buttigieg said many Democrats were critical of his decision to participate in a town hall on Fox News, but added that he believes the party needs to meet voters where they are, whether it’s through Fox News or visiting places where Democrats aren’t seen much.

Buttigieg was asked about laws passed recently to ban or restrict abortion in states such as Alabama. He said he believes the right to have an abortion is “an American freedom” and that the government shouldn’t have a role in limiting it.

“I think the dialogue has gotten so caught up on where you draw the line that we’ve gotten away from the fundamental question of who gets to draw the line,” he said. “And I trust women to draw the line.”

Asked whether his position extends to the third trimester of pregnancy, Buttigieg said those late-term abortions make up a small percentage of abortions performed and asked the audience to put themselves in that woman’s shoes.

Any woman making that decision has likely been expecting to carry the baby to term, he said, and received “the most devasting medical news in their lifetime”, forcing them to make “an impossible, unthinkable choice”.

“And the bottom line is as horrible as that choice is, that woman, that family may seek spiritual guidance, they may seek medical guidance,” he said. “But that decision’s not going to be made any better medically or morally, because the government is dictating how that decision should be made.”