* Federal judge OKs attorney general's request for a stay

* Defense lawyers had argued SEC might gain unfair edge (Recasts, adds details, new paragraphs 5-15)

By Joan Gralla

NEW YORK, May 29 (Reuters) - A federal judge on Friday approved New York Attorney General Andrew Cuomo's request to delay the U.S. Securities and Exchange Commission's pension kickback case, rejecting defense attorneys' arguments that this could give the federal regulator an unfair advantage.

Cuomo, a Democrat, is investigating millions of dollars of fees investment firms paid to middlemen in return for being hired to invest some of the state's $110 billion pension fund.

The SEC is conducting a separate, civil probe of the same ties between investment firms and the agents, lobbyists and lawyers they hired.

"This litigation is a non-entity until the criminal matter is concluded in the New York State Supreme Court," said Judge Colleen McMahon, of the Southern District of New York in Manhattan, at the hearing.

Cuomo's request is common in such investigations, as prosecutors fear that defendants in criminal trials will benefit from any materials turned over to them in civil proceedings.

A New York grand jury indicted the former comptroller's fund-raiser, Henry Morris, and pension investment officer, David Loglisci. Lawyers for the two say they are innocent.