Which part of the government has the greatest authority in setting foreign policies

The part of the government that has the greatest authority in setting foreign policies is the Executive Branch.

Explanation:

The executive branch is one of the 3 branches of the Federal Government of the United States. It is formed by the President, the Vice President and the different members of the Cabinet, as well as the officers of lesser rank within said structure.

This branch is responsible for the task of administering the nation and ensuring compliance with the laws, as well as representing the country abroad and negotiating with foreign nations. It is clear from these last tasks that international politics will be carried out by the President with the advice of his various collaborators.

Answer: That would be the president or "powers of the president"