Rep. Virgil Goode, R-Va., made the comments in a letter sent to hundreds of constituents about Ellison, D-Minn., the first Muslim elected to Congress.
"The Muslim representative from Minnesota was elected by the voters of that district, and if American citizens don't wake up and adopt the Virgil Goode position on immigration there will likely be many more Muslims elected to office and demanding the use of the Koran," Goode wrote.
Goode said the U.S. needs to stop illegal immigration "totally" and reduce legal immigration.
Goode added: "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."
Ellison was born in Detroit and converted to Islam in college. He did not immediately return a telephone message left Wednesday.
The Council on American-Islamic Relations, a civil rights group, called on Goode to apologize for the letter.
"Representative Goode's Islamophobic remarks send a message of intolerance that is unworthy of anyone elected to public office," said CAIR National Legislative Director Corey Saylor. "There can be no reasonable defense for such bigotry."
Goode spokesman Linwood Duncan said no apology was forthcoming.
"The only statement the congressman has is that he stands by the letter," Duncan said.