The letter, dated 9 September, says the spread of the COVID-19 Delta variant represents a significant concern in the city, where new cases have "increased significantly" over the last two months.
It says under New York City's vaccination requirement for indoor activities, "all persons entering the UN premises for the purpose of entering the General Assembly Hall would be required to show proof of vaccination in order to gain entry to the Hall".
Individuals coming to the General Assembly must also show proof of vaccination to dine, drink, or exercise indoors at the UN headquarters complex and in the city in general.
In addition, United Nations spokesperson Stephane Dujarric said that the city of New York had offered to set up a vaccination tent outside the UN building during the General Assembly which kicked off Tuesday and will be taking place until 27 September.
Before the new requirement, the United Nations did not mandate delegates coming to the compound in Midtown Manhattan for the event to be vaccinated.