Days after the election, Gov. Andrew M. Cuomo said, “If any immigrant feels that they are under attack, I want them to know that the state of New York — the state that has the Statue of Liberty in its harbor — is their refuge.” Mr. Cuomo announced on Tuesday that a hotline had been established to report complaints of bias or discrimination.

Questions of privacy and data were at the forefront of immigrants’ concerns on Monday night. Some worried that IDNYC, the city program that provides government-issued ID cards to residents, could be turned against the undocumented.

Nisha Agarwal, the commissioner of the Mayor’s Office of Immigrant Affairs, encouraged people to continue to sign up for the free identification cards, and assured them that the city made confidentiality a priority. The city is considering expunging ID-holders’ contact information from its records, as was allowed in the 2014 law that established the program.

“A determination regarding record retention will be made by the end of the calendar year,” Rosemary Boeglin, a spokeswoman for the mayor, said.

Mr. Vargas advised the group in Port Richmond to avoid filing new applications for temporary work permits under the administrative program known as Deferred Action for Childhood Arrivals, for fear of providing personal data to the new administration. But he said that those whose permits were up for renewal should apply. Mr. Vargas, one of the first lawyers admitted to the New York State bar with a deferred action authorization, applied for renewal of his work permit on Tuesday.

Immigrant organizations across the city have begun coordinating a response to whatever immigration policies the new administration may adopt.