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Mr. Murphy is bracing for an extended legal fight.

His campaign sent a fundraising email Wednesday pleading with supporters to donate the hundreds of thousands of dollars they say it could take to go through a court battle.

Mr. West said he thinks a mix of sloppiness, incompetence and malfeasance is behind the discrepancy in the vote counts.

“The bottom line is this: We just want to make sure we get that early-voting recount done, and that’s all we asked for,” he said. “We’re asking for something that is very simple. And I think that the state should not go down the path of certifying this election until the questions of the voters are answered.”

When asked if he thinks he won the election, Mr. West responded that “someone has to explain to me a 4,400-vote swing at 1-o’clock in the morning in about a 30-to-35-minute time period.”