The president has the power to negotiate treaties with foreign nations, but such agreements on behalf of the united states must be approved by

 A two-thirds majority of the US Senate.

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Article II, Section 2 of the Constitution lays out the process for treaties made by the United States with other nations.  That section of the Constitution says of the President, "He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur."

The advice and consent of the Senate typically comes after the treaty has been negotiated by the President.  As reported by Justia (a legal information site), "The Senate’s role in relation to treaties is essentially legislative in character."  In a Supreme Court decision in 1936, this was affirmed by the Court's decision, which said, that the President "alone negotiates. Into the field of negotiation, the Senate cannot intrude" (United States v. Curtiss-Wright Export Corp., 1936).   However, for the treaty to become active, the President must secure approval by the Senate, with a two-thirds majority vote, as stipulated by the Constitution.

An article on the United States Senate's own webpage concerning "Advice and Consent of the Senate" notes that this provision in the Constitution was connected to the overall idea of separation of powers that the founding fathers had in mind.  In The Federalist Papers (#75, #76), urging ratification of the Constitution,  "Alexander Hamilton argued that the provision afforded a necessary means of checks and balances."

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