"A total loser!" Mr. Trump tweeted as he headed out for a round of golf on Thursday.
The reception to Amash's move brought a bitter rebuke from Rep. Mark Walker (R-NC).
"The @HouseGOP never left @justinamash - we simply ran out of space for his ego," Walker tweeted, adding that Amash should lose his committee assignments provided by the GOP.
Amash would be the first House member to leave one of the two parties and become an Independent since Rep. Virgil Goode switched from the Democratic Party in 2000. He later moved over to the Republican Party.
The last Independent in the House was Bernie Sanders, who served for 16 years before being elected to the U.S. Senate in 2006.
Amash got into hot water with his own party by publicly breaking with the GOP over the Mueller Report, accusing Attorney General William Barr of wrongly characterizing the findings of the investigation into Russian interference in the 2016 elections, and then calling for impeachment proceedings against the President.
"In comparing Barr’s principal conclusions, congressional testimony, and other statements to Mueller’s report, it is clear that Barr intended to mislead the public about Special Counsel Robert Mueller’s analysis and findings," Amash tweeted in mid-May.
In that same tweet, Amash complained that "Partisanship has eroded our system of checks and balances."
Amash has already drawn Republican primary opponents in his Michigan district, but he told an NPR reporter in Michigan today that he would run for re-election as an Independent.
Amash won re-election in 2018 with 54 percent of the vote.