WASHINGTON — Thom Tillis’s victory Tuesday in the North Carolina Republican Senate primary sets up a campaign against Senator Kay Hagan, a first-term Democrat, in what will be one of the nation’s most contentious and expensive races in the battle to win control of Congress.

Mr. Tillis’s conservative record as the state House speaker helped to propel him to 46 percent of the vote, enough to avoid a runoff. The challenge for Ms. Hagan, considered one of the more vulnerable Democrats in the country, will be to persuade voters that her opponent’s views are out of the mainstream in the state whose political leanings over all have become more moderate in recent years.

In an interview Wednesday morning, Mr. Tillis offered a preview of his likely response to attacks from Democrats about his tenure as speaker. “It’s a contrast between her adding taxes, adding regulations while we’re cutting taxes and reducing regulations,” he told MSNBC’s Chuck Todd.

But Chris Hayden, a spokesman for Ms. Hagan’s campaign, said, “Tillis is wasting no time proving to the outside special interests who dragged him to the finish line last night that he will be their proxy in their war against North Carolina’s middle-class families.”