In an op-ed essay in The Washington Post that did not mention Trump by name, Amash wrote: "I've become disenchanted with party politics and frightened by what I see from it. The two-party system has evolved into an existential threat to American principles and institutions."
Three hours after the essay was published, Trump responded with a personal attack against Amash, calling him "one of the dumbest and most disloyal men in Congress." Amash, 39, is known as a libertarian with a contrarian streak and has been one of Trump's staunchest critics on the right.
He has even considered a run against him in the 2020 primary election. Amash's move on Thursday makes him the only independent member of the House, which has 235 Democrats and, now, 197 Republicans.
In May, he became the first - and so far the only - sitting Republican member of Congress to join Democrats in saying that the president had committed offenses that rose to the level of impeachment.
That assertion was based on his reading of the redacted report by the special counsel, Robert Mueller III, which was released in April.
In a series of tweets, Amash accused attorney general William Barr of deliberately misrepresenting the report's findings in his summary.
Amash argued that the report had identified multiple examples of conduct that could be labelled obstruction of justice.
The president immediately struck back, attacking Amash as a "loser" and reinforcing the congressman's isolation within the Republican Party.