In January, Agema posted a comment to his Facebook page asking, "Have you ever seen a Muslim do anything that contributes positively to the American way of life?"
Amash condemned Agema's "approach," calling it a "distraction" for a party yearning to broaden its appeal to minority voters.
"Defending civil liberties is at the heart of the Republican Party and our Constitution. As I've demonstrated with my words and record, I am trying to grow a new generation of Republicans that includes more gays and lesbians, racial-ethnic minorities, women, and young people," Amash said in a statement.
"Dave's approach has become a distraction for those of us who are standing up to the political establishment, whose push for bigger government, more corporate welfare, and less individual liberty have hurt our party. I hope Dave will do the right thing for the next generation of conservatives and step down. And I hope that the politicians who are criticizing Dave will stand with me in protecting civil liberties with their votes and actions, not just their rhetoric."
Former Republican National Committeewoman Betsy DeVos on Sunday told the Detroit News that Agema should resign, and she urged party leaders to join her in condemning his comments.
"Leaders have a responsibility to create an inclusive, welcoming party, not to exclude," she said. "What's going on is cause for concern about our future prospects as a party and our ability to bring people around to our point of view and long-term agenda. We are driving people away who might otherwise support what we stand for."