Vice President Kamala Harris and former President Donald J. Trump swept through Southern states on Saturday, outlining sharply divergent economic messages for voters in top battlegrounds and, in Mr. Trump’s case, solidly blue Virginia.

Mr. Trump, after a week in which controversies often overshadowed his closing argument, traveled to North Carolina and Virginia, where he gave rambling speeches in which he tried to turn the race back toward immigration, the economy and transgender issues.

Ms. Harris began her day at a rally in Atlanta, where she focused on her plans to bolster the economy, an approach that her advisers say has been intentional in the last days of a coin-flip race.

At an event that featured food trucks and a performance by the Georgia-born rapper 2 Chainz, she said her first goal as president would be “to bring down the cost of living for you” through tax cuts and measures like expanding Medicare to help cover home care. She emphasized that message soon after at a rally in Charlotte, N.C., saying that Mr. Trump would fight for “billionaires and big corporations.”

Mr. Trump, in his speeches at an airport in Gastonia, N.C., and arenas in Salem, Va., and Greensboro, N.C., pounced on Friday’s labor report showing that employers added just 12,000 jobs last month.

“These are depression numbers, I hate to tell you,” he said in Gastonia, wildly distorting the picture of what is actually a healthy economy and leaving out that the latest figures were driven down by hurricanes and a labor strike.