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Nikki Haley won the Republican primary in Washington, D.C., on Sunday, logging her first victory after a string of losses to former President Donald J. Trump — who responded bitterly on social media, saying he had purposely avoided the contest “because it is the ‘Swamp.’”

Ms. Haley received about 63 percent of the vote to Mr. Trump’s 33 percent, according to The Associated Press, securing all 19 available delegates and becoming the first woman ever to win a Republican presidential primary. But Mr. Trump remains well positioned to lock down the nomination later this month.

The contest in Washington was tiny: Just over 2,000 Republicans voted in the overwhelmingly Democratic city, compared with 110,000 in Iowa, 325,000 in New Hampshire and 757,000 in South Carolina.

Ms. Haley seemed to acknowledge that in a post on X. “Thank you, DC!” she wrote. “We fight for every inch.”

But Mr. Trump could not let that inch go. On his social media site, he claimed falsely that Ms. Haley had “spent all of her time, money and effort there.” He never used her name, referring to her repeatedly by his disparaging “Birdbrain” nickname.

Ms. Haley sought to play the symbolism of Washington — not exactly Republicans’ favorite place — to her advantage, writing, “Republicans closest to Washington’s dysfunction know that Donald Trump has brought nothing but chaos and division for the past 8 years.”

Karoline Leavitt, a spokeswoman for Mr. Trump, said in a statement that Ms. Haley “was just crowned Queen of the Swamp by the lobbyists and D.C. insiders that want to protect the failed status quo.”

The race now turns to the 15 states that will hold Republican contests on Super Tuesday, March 5. While it is not mathematically possible for Mr. Trump to lock up the nomination just yet, he could come very close with strong performances on Super Tuesday and position himself to do so within the next couple of weeks.