The Republican Senator declared that even though Congress must respect Trump’s authority, they are “not his subordinates [and] we don’t answer to him”.
Mr McCain, who has openly criticised the President’s actions in the past, also urged Congress to keep the Republican firebrand in check.
Writing for the Washington Post, he said: “That has never been truer than today, when Congress must govern with a president who has no experience of public office, is often poorly informed and can be impulsive in his speech and conduct.
“We must respect his authority and constitutional responsibilities. We must, where we can, cooperate with him.
“But we are not his subordinates. We don’t answer to him. We answer to the American people.

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“We must be diligent in discharging our responsibility to serve as a check on his power.”
He added: “Congress will return from recess next week facing continued gridlock as we lurch from one self-created crisis to another.
“We are proving inadequate not only to our most difficult problems but also to routine duties”
The decorated Vietnam War hero also hit out at Trump’s prosed Mexican border wall, which the President continues to push for funding from Congress.
Mr McCain said: “A literal wall might not be the most effective means to that end, but we can provide the resources necessary to secure the border with smart and affordable measures.
“Let’s make it part of a comprehensive bill that members of both parties can get behind — one that values our security as well as the humanity of immigrants and their contributions to our economy and culture.”
Yesterday the nation’s Customs and Border Protection agency announced it had awarded contracts, worth up to £386,000 ($500,000) each, to four construction firms for prototypes.
All four companies selected so far are based in the US, in the Mexico border states of Alabama, Arizona, Texas and Mississippi.
Ronald Vitiello, acting deputy commissioner of Customs and Border Protection, said the concrete prototypes would be 30ft long and up to 30ft high. He added: “Today we mark a significant milestone.”
The prototypes are expected to have “anti-climb” features to deter illegal immigrants from sneaking into the US.
And construction is expected to begin in two weeks, and to be completed 30 days later.