Goode came under fire for sending his central Virginia constituents a letter criticizing a request by Rep.-elect Keith Ellison, D-Minn., to be sworn in using the Koran instead of the Bible next month.
"I fear that in the next century we will have many more Muslims in the United States if we do not adopt the strict immigration policies that I believe are necessary to preserve the values and beliefs traditional to the United States of America and to prevent our resources from being swamped," Goode wrote.
Ellison is the first Muslim to be elected to Congress, and could not be reached by The Washington Post for comment Wednesday.
Meanwhile, the Council on American-Islamic Relations asked Goode to apologize, with spokesman Corey Saylor calling Goode's remarks "bigotry" unsuited to an elected official, CNN reported.
"Rep. Goode's Islamophobic remarks send a message of intolerance that is unworthy of anyone elected to public office," Saylor said in a statement.