UNITED NATIONS — As the growing feud between City Hall and the United Nations intensified yesterday over safety conditions at the Turtle Bay landmark building, a former New York governor, George Pataki, roamed the U.N. corridors in a new role, positioning him as a potential mediator. “I don’t want to make it look like I’m Henry Kissinger doing shuttle diplomacy here,” Mr. Pataki, who serves as one of three American public delegates to the U.N. General Assembly session currently taking place, told The New York Sun yesterday. He did set up some meetings between U.N. and city officials, however. “I have close ties to the city administration and understand the issues,” he said, while “I also work as a U.S. public advocate and I’m working closely with the U.N.”

Mr. Pataki added that he understands Mayor Bloomberg’s concerns. The latest stage in the increasingly public exchange between the city and the United Nations was a letter sent yesterday by the city’s commissioner for the United Nations, Marjorie Tiven, to the U.N. administration chief, Alicia Barcena.

In the letter, Ms. Tiven, who is Mr. Bloomberg’s sister, wrote that the implementation of safety measures — such as the construction of a separation barrier between buildings and the installation of smoke detectors by the United Nations — lags behind schedule, which had been confirmed in past meetings with city officials. “That is not satisfactory,” Ms. Tiven wrote.

In her letter, answering an earlier communication from Ms. Barcena, Ms. Tiven repeats the mayor’s previous threat that if deadlines for agreements regarding safety installations are unmet, the city would order all school trips to the building canceled and “if warranted, the city will take further action as well.” Ms. Tiven added that she hoped such actions are not needed, but the city “must do everything necessary to create safe environment, of which the U.N. is certainly a vital part.”

As an international entity where America has no jurisdiction, the United Nations is “not part of this country, I guess it’s an independent land,” Mr. Bloomberg told reporters yesterday. Therefore, he added, “we can’t enforce our building codes” on the U.N. headquarters building. Nevertheless, he said, “we do have the responsibility to people going in there, particularly our children.”

And as Mr. Pataki noted, “It’s not going to be the U.N. firefighters if there is a fire in the building — it’s going to be the NYC firefighters.” The city therefore was correct in pushing an “accelerated time table” to resolve nearly 900 fire code violations that plague the First Avenue building, he said.