Fannie-Freddie Debt Elimination Act of 2013 - Requires any amounts paid or repaid to the Secretary of the Treasury by the Federal National Mortgage Association (Fannie Mae) or the Federal Home Loan Mortgage Corporation (Freddie Mac) to be transferred to the special Treasury account into which money received as gifts and proceeds from the sale or redemption of gifts is deposited for reduction of the national debt.

Prohibits the Secretary from entering into any agreement to further alter, amend, or change any provision of the Amended and Restated Senior Preferred Stock Purchase Agreements referred to by this Act that relates to dividend payment dates, dividend periods, dividend rates, or dividend amounts.