The offer came nearly three weeks after the 5,300-pound granite monument was removed from the rotunda of the state judicial building to comply with a federal judge's order. Moore refused to follow the order, but Alabama's eight associate justices overruled him.
Since the monument's removal, Moore has criticized U.S. District Judge Myron Thompson of Montgomery and the 11th U.S. Circuit Court of Appeals for ruling that the monument is an improper governmental endorsement of religion.
"By its very action as the elected representatives of the American people, Congress would restore the balance of power between the branches of government and would send a message to federal courts that we, the people, have the final word on our inalienable right to acknowledge God," Moore said in a statement.
Moore met with several members of Congress last week in Washington to discuss public displays of the Ten Commandments, said his spokeswoman Jessica Atteberry. She declined to identify the lawmakers.
Alabama Sen. Richard Shelby issued a statement calling on Congress to accept Moore's "gracious offer." A spokesman for House Speaker Dennis Hastert said the speaker had no comment because Moore had not sent him a formal invitation to take the monument. But he noted that Hastert keeps a copy of the commandments in his office.
Ayesha Khan, an attorney for one of the groups that sued to have the monument removed from the judicial building, said Moore's request "shows the same level of disregard for federal taxpayers as he has shown all along for Alabama state taxpayers."
Moore, who was suspended for refusing to comply with a federal court order, has declined offers to display the monument in Mississippi and North Carolina.