UNITED NATIONS -- The United Nations General Assembly created a new counterterror office Thursday, which was adopted in a resolution by acclamation. Diplomats say the office is expected to be led by a Russian official.

While investigations in Washington have been focused around meetings between Trump associates and Russia's Ambassador to the U.S., Sergey Kislyak, he has put his name in the mix to run the new office -- a high level job that would put Kislyak in the inner circle of U.N. Secretary General Antonio Guterres.

Several diplomats say the U.S. has not put up much of a fight against Russia running the office due to the fact that this position was created by the General Assembly, not the Security Council. Therefore, the U.S. does not have a right to veto.

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Matthew C. Waxman, faculty chair of the program on Law and National Security at Columbia Law School, told CBS News that President Trump "has signaled that he wants to work more closely with Russia on counterterrorism."

With the new counterterror office approved, the secretary general will appoint a leader. Two Russian candidates -- Kislyak and Andrey Krutskikh, who is a cybersecurity expert and senior advisor to the Kremlin -- appear to be in the running for the job as U.N. counterterrorism czar.

If Kislyak is hopelessly embroiled in Washington, D.C. in the coming weeks, Russia may turn to either Krutskikh, Deputy Foreign Minister Vasily Nebenzya or Deputy Foreign Minister Anatoly Antonov.

In an interview with Fox News, U.S. Ambassador to the U.N. Nikki Haley expressed her concerns about a Russian leading the new office. "I don't want to see them get it. That's not something we would cheer for, but I wouldn't be surprised if they got it," she said.

The U.N. resolution adopted Thursday establishes the office of counterterrorism and transfers the current Implementation Task Force Office and the counterterrorism center out of the U.S.-led U.N. Department of Political Affairs, and into the new office. The resolution recognizes the "importance of countering terrorism and preventing violent extremism as and when conducive to terrorism."

In May, the General Assembly approved a budget of $15 million for the office. The budget includes funding for 2017, along with salaries for the new under secretary general and a special assistant. Existing staffing is funded by regular budget resources, including U.S. contributions, and by voluntary funds from grants that are provided by Saudi Arabia, worth $110 million.

U.N. Under Secretary General of Political Affairs Jeffrey Feltman told CBS News that existing U.N. counterterrorism programs -- such as the United Nations Counter-Terrorism Committee Executive Directorate (CTED) and the Security Council Counter-Terrorism Committee (CTC) -- report to the Security Council and will remain intact. The two other counterterrorism offices will be moved.

The new senior official responsible for counterterror will coordinate related activities across the U.N. system, and will be the chair of the current Counter-Terrorism Implementation Task Force as well as the executive director of the counterterror center, and lead the Preventing Violent Extremism (PVE) agenda.

The President of the General Assembly, Peter Thomson, opened the vote by saying, "The General Assembly meets today to renew its unwavering commitment to strengthening international cooperation and combat terrorism in all its forms."

Some diplomats argue that Russia does not hold a senior position in New York, as four out of the five permanent members do. In an unwritten agreement crafted last fall, Russia agreed to forgo its regional turn in the selection of the next secretary general in exchange for the appointment of a Russian official to lead the new office, multiple sources tell CBS News.

Another western Security Council diplomat agreed with Haley that a Russian diplomat is likely to run the office, but expressed concern. When asked by CBS News in a background briefing with reporters if this amounted to the fox guarding the chicken coop, he said, "There are a lot of animals at the U.N." He then paused and added that at the U.N., "there is even a place for foxes."