Another high-profile Democratic incumbent, Senator Brian Schatz, was locked in a tight primary race with Colleen Hanabusa, a congresswoman, which remained too close to call on Sunday. With all but two precincts reporting, Mr. Schatz held a lead of about 1,600 votes.

Tropical Storm Iselle, despite sparing the state major damage when it hit on Friday, ultimately did disrupt the election: Voting had been postponed in two precincts on the Big Island, where the storm had hit hardest and thousands of people remained without power or running water.

The nearly 8,000 voters in those two precincts would be able to vote by mail in the coming weeks if they had not already taken advantage of early voting, which meant that the bitter Senate campaign would continue a little longer. With less than 1 percent of the vote currently separating the two candidates, a recount was also possible.

The specter of Daniel K. Inouye, the late senator and war hero from Hawaii, hung over the gubernatorial and Senate races. In the last days of his life in 2012, he asked Mr. Abercrombie to appoint Ms. Hanabusa to succeed him. But Mr. Abercrombie ignored his request and instead appointed Mr. Schatz, his lieutenant governor, to complete Mr. Inouye’s term in the Senate.

Mr. Schatz and Mr. Abercrombie enjoyed strong support from the Democratic establishment, including President Obama, who grew up in Hawaii.

Ms. Hanabusa, meanwhile, repeatedly underscored her connections to Mr. Inouye, whose son attended her campaign rally on Saturday. She played up her roots in rural Hawaii, while trying to paint Mr. Schatz as a usurper who was now enjoying support from Washington. (Mr. Schatz also grew up in Hawaii.)

Image Senator Brian Schatz faced a challenge from Representative Colleen Hanabusa, but results remained too close to call. Credit... Marco Garcia/Associated Press

“This is the United States Senate race, the one to determine who would succeed Senator Inouye,” Ms. Hanabusa said. “This is the first time the people have had a say.