New York’s detainer law and policy mandates that officials turn over to ICE only those who are convicted of violent and serious offenses, and only when ICE has met legal and due process requirements.

Mr. Khan, 21, was released shortly after he was arraigned on charges of assault and criminal possession of a weapon in relation to the altercation with his father, in which the authorities said he had slashed his father with a broken coffee cup. He was arrested again last week and charged with the murder of Ms. Fuertes.

The Police Department disputed the claim, saying it did not receive a detainer request when Mr. Khan was first arrested. ICE responded by releasing a copy of the fax transmission form appended to the detainer, which was dated Nov. 27, the same day as the arrest.

“How much more do you need? Should he have beat up his mother, too? Should he kick the dog?” Mr. Albence said. “How much more do you need to take enforcement action against an illegal alien?”

A spokeswoman for Mayor Bill de Blasio called Ms. Fuertes’s death “an absolute tragedy.”

“Fear, hate and attempts to divide are signatures of the Trump Administration, not New York City. We are the safest big city in America because of our policies, not in spite of them,” said the spokeswoman, Freddi Goldstein.

Ms. Fuertes emigrated to New York from the Dominican Republic in the 1960s and was a legal resident of the United States, her son said. In recent years, she collected cans around her neighborhood of South Richmond Hill, Queens, and was described after her death as a beloved figure in her community.