HANOVER, N.H. — Former Secretary of State Hillary Clinton claimed she is the real progressive in the Democratic race for the White House during a Dartmouth College rally yesterday amid the pressure of Vermont Sen. Bernie Sanders’ sudden surge.

“I will fight against inequality,” said Clinton, who is set to march in a Fourth of July parade in Gorham today. “I have a long history of doing that. I will fight hard against what I see as the injustice and unfairness in our society. I take a back seat to no one when you look at my record of standing up and fighting for progressive values.”

The indirect shot at Sanders — who drew a crowd of nearly 10,000 people in Wisconsin on Wednesday and is expecting thousands during a town hall in Portland, Maine, on Monday — comes as the Herald reported Sen. Elizabeth Warren is keeping the door open to campaigning with the Vermont senator.

Several attendees yesterday admitted their first choice for president was actually Warren, but were divided on whether the Bay State senator should take sides in the Sanders-Clinton showdown.

“I think she would be hurting the effort in the long run if she came out for Bernie right now,” said Sarah Stewart, a summer resident of Norwich, Vt. “I’m hopeful she’ll eventually come out for Hillary.”

Stewart said she decided to back Clinton only after Warren opted not to run.

Clinton rallied attendees on the border of Sanders’ home state yesterday, but still had some work to do to seal many of their votes.

“She should be addressing what he’s saying, because he obviously has the ear of a lot of people in this country,” Sybil Buell of Norwich, who’s leaning toward Sanders, told the Herald. “I think some of these economic issues — particularly wage disparity — she might not actually have addressed outright if he wasn’t pushing her.”

Ellen Baber of Hanover looked at the burgers, potato salad and ice cream being handed out on the Ivy League campus and questioned why Clinton couldn’t pick a more working-class location ?to campaign.

“Here we are in the midst of the 1 percent holding this nice get-together,” Baber said. “I wonder why it wasn’t in Lebanon … where there’s some ordinary people.”

Asked who she was leaning toward, Baber — conscious of the Clinton crowd — leaned forward and whispered: “Bernie.”

“He says what needs to be said,” she added, conceding she doesn’t think he can actually win. “He says it the way it is.”