A Texas woman has been charged with threatening to kill Tanya S. Chutkan, the federal judge in Washington who is overseeing former President Donald J. Trump’s prosecution on charges of seeking to overturn the 2020 election.

The woman, Abigail Jo Shry, of Alvin, Texas, called Judge Chutkan’s chambers on Aug. 5, two days after Mr. Trump was arraigned on the election interference charges, and left a voice mail message attacking the judge, who is Black, with a racial slur, according to a criminal complaint unsealed on Friday.

In the message, Ms. Shry told Judge Chutkan, “If Trump doesn’t get elected in 2024, we are coming to kill you, so tread lightly, bitch,” according to the complaint. She added, “You will be targeted personally, publicly, your family, all of it.”

Ms. Shry, 43, also issued a threat against Representative Sheila Jackson Lee, a Black Democratic congresswoman from Texas, the complaint said.

Mr. Trump has a long history of verbally attacking judges and other people involved in the criminal cases brought against him, particularly on social media. The day before the call, Mr. Trump had posted a message on his social media platform, Truth Social, saying, “IF YOU GO AFTER ME, I’M COMING AFTER YOU!” (His campaign said his words were not directed against anyone involved in the election interference case.)

Late last week, Judge Chutkan addressed that issue, warning Mr. Trump that she would take measures to ensure that he did not make “inflammatory statements” about the case in a way that might intimidate witnesses or otherwise harm the integrity of the proceeding.

Almost immediately, Mr. Trump tested the boundaries of Judge Chutkan’s admonition by posting a series of messages on Truth Social that largely amplified the criticism that other people had lodged against her.

In one post, written by an ally of Mr. Trump’s, the lawyer Mike Davis, a large photo of Judge Chutkan accompanied text that falsely claimed she had “openly admitted she’s running election interference against Trump.” In two other posts, Mr. Trump wrote: “She obviously wants me behind bars. VERY BIASED & UNFAIR.”

The posts criticizing Judge Chutkan were published after Ms. Shry’s voice mail message.

When federal agents visited Ms. Shry at home three days after she left the message for Judge Chutkan, she admitted that she had called the judge’s chambers, the complaint said. Ms. Shry told the agents that she had no plans to go to Washington or to Houston, the area that Ms. Lee represents. But she also said that “if Sheila Jackson Lee comes to Alvin, then we need to worry,” according to the complaint.

Ms. Shry was denied bail on Wednesday and ordered to be held in custody for at least 30 days following a detention hearing in Federal District Court in Houston.

At the hearing, court papers said, Ms. Shry’s father, Mark Shry, testified that she was a “nonviolent alcoholic” who “sits on her couch daily watching the news while drinking too many beers.”

After drinking, Mr. Shry told a judge in Texas, Ms. Shry often became “agitated by the news” and started “calling people and threatening them,” the papers said.

Mr. Trump’s supporters have sometimes engaged in violence after officials in the criminal justice system have taken action against him.

Last summer, after F.B.I. agents descended on Mar-a-Lago, his private club and residence in Florida, hauling away a trove of classified documents, an armed Ohio man enraged by the search tried to break into the bureau’s field office near Cincinnati.

The man was ultimately killed in a shootout with the local police.