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Hillary Clinton faced criticism from both sides of the abortion debate on Monday after she waded into the fraught argument about when life begins by describing the unborn as a “person.”

Mrs. Clinton, the leading Democratic presidential candidate, made the comment during an interview Sunday on NBC’s “Meet the Press” after she was asked about abortion restrictions and the rights of the unborn.

“The unborn person doesn’t have constitutional rights,” Mrs. Clinton said.

She added: “That doesn’t mean that we don’t do everything we possibly can, in the vast majority of instances to, you know, help a mother who is carrying a child and wants to make sure that child will be healthy, to have appropriate medical support.”

Presidential candidates have been struggling to discuss the sensitive topic of abortion, and Mrs. Clinton’s remarks came less than a week after Donald J. Trump, the leading Republican candidate, came under fire for saying that abortion should be banned and that women who have abortions should be punished. He later backtracked, saying that doctors who perform abortions should be punished. Then he said that the current laws should not be changed.

A longtime advocate of abortion rights, Mrs. Clinton is often criticized by anti-abortion groups. In this case, however, she frustrated some abortion rights supporters who said that her characterization of the unborn as a person shamed women who choose to terminate a pregnancy.

“Hillary Clinton further stigmatizes abortion,” Diana Arellano, community engagement manager for Planned Parenthood of Illinois, wrote on Twitter. “She calls a fetus an ‘unborn child’ and calls for later term restrictions.”

Abortion opponents also seized on the remark as evidence of Mrs. Clinton’s hypocrisy, arguing that if a fetus can be considered a person then it should have constitutional protections.

Some people don’t have constitutional rights, says @HillaryClinton. The civil rights issue of our time. #Prolife https://t.co/QR5pHAR4s8 — Cong. Tim Huelskamp (@CongHuelskamp) April 4, 2016

Rebecca Kiessling, the spokeswoman for the Personhood Alliance, which opposes abortion, said that defining fetuses as persons should mean that they are entitled to a right to life under the 14th Amendment. She considered Mrs. Clinton’s comment to be a “big gaffe” from the abortion rights perspective.

“It’s interesting that Hillary has now recognized the unborn as person and that she wants to deny them equal protection,” Ms. Kiessling said. “You can’t have it both ways.”

Mrs. Clinton’s use of the word “person” was also seen as a rhetorical victory by those who oppose abortion and a sign that the debate was shifting in their favor.

“I was actually pretty surprised, because usually when you hear her talk it’s about the fetus,” said Tina Whittington, executive vice president of Students for Life. “To acknowledge it’s a human person, a human child, to us it’s huge.”

The Clinton campaign did not immediately respond to a request for comment.