By Susan Cornwell and Mark Hosenball

WASHINGTON (Reuters) - Democrats on a U.S. House of Representatives panel set up to investigate the 2012 Benghazi attacks will discuss resigning from the committee after Hillary Clinton testifies before it this week, a Democratic member of the panel told Reuters on Tuesday.

"That, I think, is going to be a matter of our discussion after the hearing this week: How much longer does it make sense for us to continue to participate?" Representative Adam Schiff said in an interview.

Schiff said that being part of the Republican-led Benghazi committee positions Democrats to challenge Republican leaks about their long-running probe. He said Democrats at a long-awaited hearing with Clinton, the front-runner in the Democratic presidential primary campaign, will ensure proceedings are fair.

But the California congressman added, "At the same time, you know, we lend legitimacy, by being there, to a committee that really has none."

Asked whether Democrats should remain, Mike Pompeo, a Republican member, said in an interview he hoped they would "perform their duty to the Constitution and the Congress" by helping complete a "fact-based inquiry."

Clinton is scheduled to testify before the committee on Thursday about her handling of the attacks while secretary of state, her controversial private email server and Obama administration Libya policy.

Four people, including U.S. Ambassador Chris Stevens, were killed when militants attacked a U.S. consular facility and nearby CIA base on Sept. 11, 2012, in Benghazi, Libya.

After months of criticism from Democrats that the panel is a partisan project bent on hurting Clinton's candidacy, the committee has been on the defensive since No. 2 House Republican Kevin McCarthy said recently that the panel had helped to drive down Clinton's presidential polling numbers.

Schiff's comments came amid signs that the panel may be refocusing its efforts more on the Benghazi attacks and less on Clinton. A source familiar with its preparations for her testimony said the panel had recently pressed the U.S. State Department for clearance to make public certain emails related to security measures at the U.S. installations in Benghazi.

In recent days, partisan wrangling over the panel has intensified, with Democrats rejecting a Republican charge that Clinton mishandled secret information on her private email server. Republicans alleged that Clinton received an email containing the name of a secret CIA source in Libya. But the CIA told the committee it did not consider the name of the source, former Libya spy chief Moussa Koussa, to be secret.

(Additional reporting by Jonathan Allen; Editing by Kevin Drawbaugh and Jonathan Oatis)