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"Democrats can compete and win everywhere," Perez told "This Week" co-anchor Martha Raddatz in an interview Sunday. "That's what we showed last week not just in New Jersey and Virginia, but in mayor's races and state senate races."
Democrats won governorships in Virginia, with the victory of Ralph Northam, and New Jersey, where Phil Murphy came out on top.
Perez said it is the first time since 2005 that Democrats won the governor's office in both states.
The next race getting national attention is the Alabama election on Dec. 12 for the U.S. Senate seat that Jeff Sessions vacated when he became U.S. attorney general.
The spotlight on that race intensified this week with allegations first reported by the Washington Post that Republican candidate Roy Moore initiated a sexual encounter with a 14-year-old girl when he was 32 and also pursued three girls between the ages of 16 and 18 when he was in his 30s.
Moore has forcefully denied the allegations and dismissed calls to step aside as a candidate.
In light of the allegations against Moore, Raddatz asked Perez on "This Week" if the Democratic candidate, Doug Jones, has a real chance to win the Senate seat in deep-red Alabama.
"Doug Jones is undeniably the underdog there," Perez responded. "But I've known Doug for almost 20 years. And Doug is a man of integrity. He has been a fighter. When he was U.S. attorney, he got confirmed by a Republican Senate."
He also said that Democrats have "increased our investment in state parties by a third because when we are investing and organizing, when we are investing in good candidates, and when we lead with our values, we can compete everywhere.”
Raddatz asked the DNC chair about a recent ABC News/Washington Post poll showing that 61 percent of Americans say Democratic leaders are mainly criticizing Trump, not presenting alternatives.
Perez countered that the party's candidates led with "our values" in the 2017 elections.
"We were leading with our values in Virginia and elsewhere. We talked about health care a lot because health care is a right for all, not a privilege," he said. "The number one issue for voters in Virginia was health care. They understand that the Republicans are trying to take their health care away.”