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COLUMBIA, S.C. — Senator Bernie Sanders of Vermont began his day of campaigning Wednesday by criticizing Hillary Clinton’s support of welfare reform in 1996, accusing her of backing legislation that ultimately increased poverty levels and led more Americans to face economic anxiety.

Mr. Sanders said Mrs. Clinton helped round up votes to pass the Personal Responsibility and Work Opportunity Reconciliation Act, the welfare reform legislation that President Bill Clinton signed into law. The senator said the bill hurt Americans by punishing poor people rather than helping them. He added that if elected he would work especially hard to lower the poverty rate of the United States, increase wages, and provide health care for all people.

“What welfare reform did, in my view, was to go after some of the weakest and most vulnerable people in this country,” Mr. Sanders said. “And, during that period. I spoke out against so-called welfare reform because I thought it was scapegoating people who were helpless, people who were very, very vulnerable. Secretary Clinton at that time had a very different position on welfare reform — strongly supported it and worked hard to round up votes for its passage.”

Mr. Sanders said that since the legislation was signed into law, the number of families living in extreme poverty has more than doubled. He said that if elected, he would work to reverse that trend.

“What we are going to do in this country if I have anything to say about it is to say if somebody works 40 hours a week, that person is not going to live in poverty,” Mr. Sanders said , adding that he would raise the federal minimum wage to $15. “Today the minimum wage of $7.25 is nothing less than a starvation wage.”

Maya Harris, a senior policy adviser in Mrs. Clinton’s campaign, responded to Mr. Sanders’s criticism by saying under Mr. Clinton’s administration, the black “child-poverty rate fell 25 percent, the unemployment rate was nearly cut in half, and the median income of African-American families increased by more than 30 percent.”

In a statement, Ms. Harris added, “The original intent of welfare reform was to advance this progress, and it was done with a package of reforms.” She cited the Earned Income Tax Credit, a federal tax credit for low- and moderate-income working people, job training and child care, “so people would have the tools they needed to find work and take care of their families.”

Ms. Harris went on to explain the welfare reform law’s shortcomings, like the five-year lifetime limit, which she said Mrs. Clinton has pledged she would work to address going forward.

“When it comes to lifting more African-Americans out of poverty,” Ms. Harris said, “it has been Hillary Clinton, not Bernie Sanders, who has put forward bold plans to create good-paying jobs, dismantle the school-to-prison pipeline, and remove barriers to sustainable home ownership.”

Mr. Sanders on Wednesday also promoted his plan to create a single-payer Medicare system for all, and said that providing health care would take “a huge bite” out of poverty.

Looking ahead to the next nominating contests, he said he expects to do far better than people expect in the race and that thinks he has a good chance to pick up more delegates than Mrs. Clinton as the race goes on.