Colorado congresswoman Lauren Boebert looks set to return to Washington after her Democratic challenger called her to concede the race on Friday.
The surprisingly tight House contest is still expected to head to a recount.
Ms Boebert led by just 551 votes of nearly 327,000 counted as of Thursday evening, said the Associated Press.
The 0.16% margin qualifies for an automatic recall under Colorado state law, which would delay an official call in the race.
Speaking on Friday, 10 days after last week's midterm elections, Democrat Adam Frisch, 55, told supporters that he did not expect a recount to help him overtake Ms Boebert, a Republican.
"It would be disingenuous and unethical for us, or any other group, to continue to raise false hope and to encourage fundraising for a recount," he said.
"Please, save your money for your groceries, your rent, your children."
Ms Boebert said on Twitter that she was "so happy" to declare victory in the race.
The fight over Colorado's third congressional district had widely been expected to be a cakewalk for Ms Boebert, 35, a Donald Trump loyalist from the hard right wing of her party.
Her district, which covers almost all of Colorado's western half, is staunchly conservative, and voters there have favoured the Republican presidential candidate for the past 20 years.
The constituency has become even more red since Ms Boebert was first elected in 2020, thanks to a recent round of redistricting. Polling site FiveThirtyEight put her odds of an election victory at 97%.
Mr Frisch, a former city councillor in Aspen, worked to put space between himself and his Democratic party during the campaign, calling himself a "conservative businessman".
"I'm trying to get over the Democratic party brand," he told the BBC last month. "It's not a great brand in rural America."
In her first two years in Washington, Ms Boebert, a former restaurant owner, endeared herself to the Republican base with her combative style.
The gun-rights advocate vowed to come to Congress with her handgun in tow, picked regular fights with her Democratic colleagues, and questioned the legitimacy of the 2020 presidential election.
But it was clear that some moderate Republicans and independent Coloradans had grown frustrated with Ms Boebert. Her opponent in the Republican primary, Don Coram, went so far as to endorse Mr Frisch.
Ms Boebert has blamed her party for the close race, telling CNN recently that the Republican leadership failed to support her campaign.
It also came amid a failure by Republicans – who narrowly gained control of the House while Democrats retained the Senate – to achieve more sweeping victories in the midterms.
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