CONCORD, N.H.—New Hampshire voters will cast their ballots in the nation’s first Democratic presidential primary on Tuesday as polls show Sen. Bernie Sanders is looking to take the upper hand in the crowded contest for the party’s nomination.

Mr. Sanders, who represents neighboring Vermont, has enjoyed the top position in surveys of voters here for weeks. Pete Buttigieg, the former mayor of South Bend, Ind., has surged into the second position, riding momentum after the two men virtually tied in last week’s caucuses in Iowa.

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