Rallying supporters in two battleground states, Vice President Kamala Harris signaled on Friday that her closing campaign message would focus on the life-or-death risks that abortion bans pose to American women — and on the argument that former President Donald J. Trump is to blame.

In Madison, Wis., a crowd that had been ebullient suddenly grew hushed as Ms. Harris spoke about her visit with the family of a Georgia woman who died of sepsis after waiting for more than 20 hours for medical care to treat an incomplete medication abortion.

“She was a vibrant 28-year-old,” Ms. Harris said. “Her name, Amber Nicole Thurman, and I promised her mother I would say her name every time.”

Earlier in the day, Ms. Harris traveled to Georgia, where Ms. Thurman and another woman, Candi Miller, died after delays in medical care tied to state abortion restrictions, according to reporting by ProPublica. Their deaths occurred in the months after Georgia passed a six-week ban made possible by the Supreme Court decision overturning Roe v. Wade.

In Atlanta, Ms. Harris condemned the deaths of the two women in an impassioned speech, saying that Mr. Trump had caused a “health care crisis” and that women were being made to feel as “though they are criminals.”

Ms. Harris’s stops in the two battleground states capped a relatively smooth week for her campaign as Mr. Trump again caused or confronted several politically unhelpful headlines and controversies. Most strikingly, the Republican candidate for governor of North Carolina, whom Mr. Trump has praised as “Martin Luther King on steroids,” was found to have called himself a “Black Nazi” and praised slavery in a pornographic chat room.