Rushdie was stabbed in the neck and stomach on stage in front of a stunned audience on August 12 by 24-year-old New Jersey resident Hadi Matar.
The mayor was interacting with people from the Telugu community as part of the Batukamma festival.
Alcaraz plays American Frances Tiafoe on Friday for a spot in Sunday's final.
The attack on Rushdie triggered global condemnation and an outpouring of support for the author.
The attack on Rushdie was met with shock and outrage from much of the world, along with tributes and praise for the award-winning author.
Rushdie has long faced death threats for "The Satanic Verses," viewed by some Muslims as containing blasphemous passages. The book was banned in many countries with large Muslim populations.
As India celebrates its 75th anniversary of Independence, Left or Right, it might be a good idea to examine if the victim in New York taking a knife to an India-born novelist's head is actually just?
Rushdie has long faced death threats for his novel, "The Satanic Verses." Some Muslims said the book contained blasphemous passages. It was banned in many countries upon its 1988 publication.
The incident happened in the South Ozone Park neighbourhood, which is next to Richmond Hill where two Sikh men had been assaulted in April in what police classified as hate crimes.
This is despite the fact that Senate minority leader Mitch McConnell, Republican from Kentucky, supports the laws in principle.