He claimed Mr Trump had “engaged in specific actions” that “meet the threshold for impeachment”.
Mr Amash accused Attorney General William Barr of misleading the public about Special Counsel Robert Mueller’s findings on Russian interference.
The president responded by calling Mr Amash “a total lightweight” who was attempting to make a name for himself.
Mr Mueller’s report found no criminal conspiracy between Trump’s 2016 election campaign and Russia.
However it did find 10 instances where Mr Trump possibly attempted to impede the investigation.
Mr Amash, a representative for Michigan, made the comments on Saturday on Twitter.
Here are my principal conclusions:
1. Attorney General Barr has deliberately misrepresented Mueller’s report.
2. President Trump has engaged in impeachable conduct.
3. Partisanship has eroded our system of checks and balances.
4. Few members of Congress have read the report.
— Justin Amash (@justinamash) May 18, 2019
He told his followers that “few members of Congress even read Mueller’s report” and claimed that they made up their minds based on “partisan affiliation.”
Rashida Tlaib, a Democrat lawmaker for Michigan, asked Mr Amash to “cosponsor” an impeachment investigation resolution.
On Twitter, Mr Trump called Mr Amash a “loser”, saying that if the congressman had “actually read the biased Mueller report” he would have seen “that it was nevertheless strong on No Collusion and, ultimately, No Obstruction.”
“How do you obstruct when there is no crime and, in fact, the crimes were committed by the other side?” he added.
The 448 page report by the special counsel includes large swathes of redactions and a subpoena demanding its full version has been issued.
Many Democrats, including presidential hopeful Senator Elizabeth Warren, have called for Mr Trump’s impeachment.
Following the release of the report, she said: “The severity of this misconduct demands that elected officials in both parties set aside political considerations and do their constitutional duty.”
However House Majority Leader Steny Hoyer and House Speaker Nancy Pelosi have warned against it.
Mr Hoyer told CNN that impeachment would not be “worthwhile”. He said: “Very frankly, there is an election in 18 months and the American people will make a judgement.”
Nancy Pelosi told the Washington Post that impeaching Mr Trump is “just not worth it.”