By Wednesday night, officials had not projected which other candidate had earned enough votes to make it to the top four and therefore advance to the general election.
With 82 percent of the votes reporting, Palin had 28 percent of the vote, compared to Begich with 19 percent and Gross with 13 percent.
Democrat Mary Peltola, an Alaska Native and former state legislator who directs an intertribal fish commission, is currently on track to win the fourth and final spot in the special general election.
Alaska is having the wildest election of 2022
Palin declared victory on Saturday after the first of four ballot counts showed her solidly ahead of the other 47 candidates vying for the federal seat. Palin had an endorsement from former president Donald Trump and name recognition in a crowded field.
“I am looking forward to the special general election so we can highlight our ideas for fixing this country,” she tweeted Saturday, discussing “the right to keep and bear arms, and restoring respect for individual liberty and the Constitution.”
Begich, endorsed by the state GOP, launched his campaign while Young was still alive, casting himself as the more conservative candidate although he is from an Alaska family famous in state Democratic politics.
In a Wednesday interview with The Washington Post, Begich said he was excited by the results and expects to see even more support in the special general election from Alaskans who voted for candidates who did not make the final four.
“I have spent a career building businesses and creating jobs,” he said. “Sarah Palin’s greatest source of income right now is the website Cameo. She makes celebrity videos for a living and is essentially a human Hallmark card. That is a huge contrast.”
Sarah Palin takes early lead in crowded House race in Alaska
The Alaska Division of Elections has two more ballot counts scheduled, with the aim of certifying the election June 25.
Voters will select Young’s longer-term successor through another election, which starts with a pick-one primary also scheduled for Aug. 16 and ends with a ranked-choice vote in November. More than 30 people are running.
Hannah Knowles contributed to this report.