Story highlights Brennan will testify before the House intelligence committee in public first

Republicans and Democrats agreed more than a month ago to bring in Brennan

Washington (CNN) Former CIA Director John Brennan is set to testify before House Russia investigators next Tuesday as the question of Moscow's possible coordination with the campaign of President Donald Trump continues to engulf the Capitol.

Brennan will testify before the House intelligence committee in public first and, immediately after that, in a classified hearing.

Republicans and Democrats agreed more than a month ago to bring in Brennan and former acting Attorney General Sally Yates in a public hearing as part of the committee's reset in the wake of House Intelligence Chairman Devin Nunes' clandestine meeting at the White House.

As part of the deal, Republicans agreed to reschedule a hearing with Brennan and Yates and Democrats agreed to support bringing back former FBI Director James Comey for closed-door testimony May 4 -- five days before Trump fired him.