(Updates with comment from House general counsel, background on STOCK Act)

By Nate Raymond, Jonathan Stempel and Sarah N. Lynch

NEW YORK/WASHINGTON, June 20 (Reuters) - A U.S. judge on Friday directed the House Ways and Means Committee and a staffer to appear at a July 1 hearing to address their alleged refusal to respond to U.S. Securities and Exchange Commission subpoenas as part of an insider trading probe.

The order by U.S. District Judge Paul Gardephe in New York covers both the committee and Brian Sutter, staff director for its healthcare subcommittee, and came at the SEC's request.

The SEC said it is examining whether material nonpublic information concerning an April 1, 2013 announcement by the Centers for Medicare and Medicaid Services of 2014 reimbursement rates for a Medicare program was leaked improperly, and whether anyone traded on that information.

The case could prompt a courtroom showdown between the SEC's authority to enforce U.S. securities laws against Congress' power to manage its own affairs.

"This cannot be good for inter-governmental relations between the SEC and Congress," said Bradley Bondi, a partner at Cadwalader, Wickersham & Taft and former counsel to two SEC commissioners.

The House committee has resisted the subpoenas, in part by arguing that the U.S. Constitution shields lawmakers from having to testify or turn over documents.

"The SEC subpoenas run seriously afoul of the Constitution's Speech or Debate Clause, and we expect to respond in due course on that ground, among others," Kerry Kircher, general counsel for the House of Representatives, said in an email.

In a letter later Friday, Kircher asked Gardephe for additional time beyond July 1 to respond to the SEC.

Sutter's lawyer declined comment.

The court filings followed earlier reports of an insider trading investigation into whether congressional staff helped tip traders about the CMS announcement.

"Immunity will be the focal point of the legal controversy," said Karl Manheim, a professor at Loyola Law School in Los Angeles.

HEALTH STOCKS

The initial SEC subpoena to the House committee was previously disclosed by the committee's chairman, Rep. David Camp (R-Mich.), according to the May 9 Congressional Record.

That same day, Sutter disclosed receiving subpoenas from the SEC and a grand jury in Manhattan.

In court papers on Friday, the SEC said it was looking into an email a lobbyist at the law firm Greenberg Traurig sent to broker-dealer Height Securities regarding a deal struck in Congress about the Medicare rates.

It said that email was 70 minutes before CMS announced the rates after U.S. markets closed, and about 30 minutes before Height issued a report suggesting that the change could help companies such as Humana Inc and Health Net Inc.