WASHINGTON — Challenged by Republicans, Supreme Court nominee Elena Kagan said Tuesday the Pentagon’s recruiters had access to Harvard Law School students “every single day I was dean” and rejected GOP claims she maneuvered to thwart them.

“I’m just a little taken aback by the tone of your remarks because it is unconnected to reality,” retorted Sen. Jeff Sessions of Alabama, first Republican member of the Senate Judiciary Committee to question in public President Barack Obama’s choice for the high court.

Said Kagan: “I respect and indeed I revere the military.”

The exchange came little more than an hour into a scheduled full day of questioning by members of the panel, which will vote first on Kagan’s appointment to succeed retiring Justice John Paul Stevens. Barring a major gaffe, the 50-year old Obama administration solicitor general appears well on her way toward confirmation in time to take her seat before the court opens a new term in October.

Kagan also spoke favorably of televising Supreme Court proceedings. “It would be a great thing for the court, and it would be a great thing for the American people,” she said.