Judge Afiuni, 48, spent more than a year in a women’s prison where other prisoners threatened to kill her and tried to force her into sex.

In February, she underwent a total abdominal hysterectomy at a cancer hospital here and was moved to house arrest. She is still prohibited from speaking to the news media.

Judge Afiuni’s arrest increased concern here over the intimidation of judges and the nation’s lack of judicial independence.

Mr. Chomsky’s decision to go public with a request for her release came after months of quiet mediation on the case between the Carr Center for Human Rights Policy at Harvard University, which asked Mr. Chomsky last year to intervene, and senior government officials.

“We’re just requesting clemency on humanitarian grounds,” Mr. Chomsky, a prominent left-wing political commentator, said in a telephone interview. “She was treated quite badly; there’s no real dispute about that.” While Mr. Chomsky said her living conditions had improved under house arrest, he cited the “fragility of the charges” against her and called for her release.

Mr. Chávez ordered Judge Afiuni’s arrest after she freed a businessman jailed on charges of circumventing currency controls. His pretrial detention had exceeded Venezuela’s legal limits, and the judge said she was following United Nations guidance.

Mr. Chomsky’s public involvement puts Mr. Chávez in a difficult situation. Mr. Chávez has lauded Mr. Chomsky’s political writings, holding up a copy of his “Hegemony or Survival: America’s Quest for Global Dominance,” a critique of American foreign policy, in a 2006 appearance at the United Nations.

State media here publish interviews with Mr. Chomsky on a range of issues, and Últimas Notícias, a widely circulated newspaper, runs a column Mr. Chomsky writes. Mr. Chávez met with him here in 2009, and this year put Mr. Chomsky’s name forward as a possible United States ambassador to Venezuela.

Referring to Mr. Chomsky as “someone whose voice could be heard in Venezuela,” Leonardo Vivas, coordinator of the Latin American initiative at the Carr Center, said Mr. Chomsky had been quick to accept the center’s invitation.

Regarding the president’s own serious health problems, which Mr. Chávez disclosed Thursday in a short televised address from Havana, Mr. Chomsky said he wished him a swift and complete recovery.

Mr. Chomsky’s willingness to press for Judge Afiuni’s release shows how the president’s aggressive policies toward the judiciary have stirred unease among some who are generally sympathetic to Mr. Chávez’s socialist-inspired political movement.

As early as 2004, human rights groups expressed concern over policies here aimed at stripping the Supreme Court of its autonomy and undermining judicial independence. Mr. Chávez and his followers exert control over every political institution of importance in Venezuela, including the Supreme Court, the National Assembly and Petróleos de Venezuela, the national oil company.

“I hope that a move toward clemency with Judge Afiuni would be a step towards the importance of maintaining a properly functioning justice system,” Mr. Chomsky said in the interview. He also pointed out that Venezuela was not alone in facing a situation in which judges felt a sense of intimidation in carrying out their duties.

Mr. Chomsky went further in his public letter about Judge Afiuni, drafted with the help of the Carr Center. “The dramatic erosion of her health and the cruelty displayed against her, all duly documented, left me greatly worried about her physical and psychological well-being, as well as about her personal safety,” he wrote.