Final answer:
The president claimed executive privilege as a basis for the government's request for prior restraint against The New York Times and The Washington Post. The Supreme Court, in New York Times Co. v. United States, ruled that the government's arguments did not outweigh the First Amendment's freedom of the press, allowing the Pentagon Papers to be published.
Step-by-step explanation:
The government's request for a prior restraint on The New York Times and The Washington Post to prevent publication of the Pentagon Papers was based on the claim that the president had executive privilege to seek such a restraint. The concept of executive privilege, not enumerated in the Constitution, was historically used to protect the confidentiality of the executive branch's communications and assure that the president can secure candid advice from advisors.
However, in the landmark case New York Times Co. v. United States, the Supreme Court ruled that the government's desire to keep the Pentagon Papers classified was not strong enough to override the First Amendment's freedom of the press.
With the classification of the Pentagon Papers as a matter of national security, the government argued that their publication could endanger the United States. However, the Court maintained that prior restraint is rarely justified and that in this instance, the government did not prove that national interests would be harmed by the release of the documents. Therefore, the publications were allowed to proceed.