In South Texas, Jessica Cisneros calls for a recount in her primary runoff against Representative Henry Cuellar.

Jessica Cisneros, the progressive South Texas immigration lawyer, said on Monday that she would formally demand a recount in her razor-thin runoff against Representative Henry Cuellar, the nine-term incumbent and moderate Democrat she has been trying to unseat for years.

“I owe it to our community to see this through to the end,” Ms. Cisneros said in a statement.

The May 24 election has not been called by The Associated Press. As of Friday, Mr. Cuellar was ahead of Ms. Cisneros by 187 votes.

The Cisneros campaign said the Texas Democratic Party canvassed and certified the results of the runoff on Monday, and the review showed Mr. Cuellar ahead of Ms. Cisneros by 281 votes. Mr. Cuellar’s campaign had already declared victory the day after the runoff, saying that the margin of victory at that time “will hold.”

In a statement on Monday, Mr. Cuellar said, “Every vote has been counted and our margin not only held but increased.” He added, “As Democrats, it is now time to come together and win the general election in November.”

Mr. Cuellar said Ms. Cisneros had “every legal right” to demand a recount, but he said that she “has no path to victory and will not gain 281 votes.”

Ms. Cisneros has until 5 p.m. Wednesday to formally submit a recount request to the Texas Democratic Party, which in turn has 48 hours to review the matter, according to a spokeswoman for the party. The spokeswoman, Rose Clouston, said that once the request was received and deemed eligible, the process of recounting the ballots could begin immediately.

The race has drawn national attention as Representative Alexandria Ocasio-Cortez and other progressive leaders have backed Ms. Cisneros’s attempt to unseat one of the most conservative Democrats left in the House. Mr. Cuellar campaigned alongside Representative James E. Clyburn, the House majority whip, and faced scrutiny over a federal investigation. The F.B.I. raided Mr. Cuellar’s Laredo home earlier this year as part of an investigation that appears to be linked to an inquiry into the political influence of Azerbaijan, the former Soviet republic.

Ms. Cisneros’s demand for a recount on Monday was the latest chapter in her efforts to defeat Mr. Cuellar, for whom she had once worked as an intern. In 2020, Ms. Cisneros came within 2,700 votes of victory. This year, she challenged him again, holding him just below the 50 percent threshold in the March primary to avoid a runoff.

In Texas primaries, any candidate who finishes below 50 percent faces the No. 2 vote-getter in a runoff. In the Democratic primary in March, Mr. Cuellar won 48.4 percent of the vote, Ms. Cisneros got 46.9 percent and another liberal candidate, Tannya Benavides, had 4.7 percent.