Donald J. Trump, looking to amass as many votes as possible in the South Carolina primary, is increasingly trying to appeal to the state’s black voters. In doing so, he appears to hope that any memory of his 2011 demand to see the birth certificate of the nation’s first black president is a distant one.

At a news conference on Monday in South Carolina, where residents can vote in either party’s primary, Mr. Trump handled a question about undocumented immigrants, many of whom are Hispanic, by bemoaning the plight of African-Americans under President Obama.

“I’m a unifier,” Mr. Trump said. “Obama is not a unifier.”

The candidate whose campaign pillar has been taking a hard line on undocumented immigrants and who has used caustic language about Mexicans turned to a woman who asked him about “Dreamers,” the term used for children of undocumented immigrants who were not brought to the country of their own volition. “I want dreamers to come from this country,” Mr. Trump said.