House Democrats will meet privately with National Security Adviser Condoleezza Rice on Wednesday, a week after the senior White House adviser gave face time to the rest of Congress to discuss the Iraqi conflict.

On Thursday morning Rice met with House Republicans, followed by separate sessions with Senate Republicans and Senate Democrats.

House Democrats will meet with Rice Wednesday afternoon in a closed-door, Members-only Caucus meeting, called specifically for her visit. The national security adviser last week offered to brief the House Democrats after House Republicans invited her to meet with their Conference, GOP and Democratic leadership aides said.

House and Senate Democrats alike said they welcome the chance to talk with Rice, but say they are disappointed they were contacted after meetings with House and Senate Republicans were already scheduled. Congressional Democrats also are angry that the White House chose to hold separate sessions with Members, rather than meetings in a bipartisan format.

“We don’t know if they are providing additional information to the Republicans,” said one House Democratic leadership aide. “If they don’t want to politicize this, why not have her come before the entire Congress?”

Republican Members and aides alike, however, argued that the White House should be able to have separate consultations with the parties on key issues, noting the meeting was not a “security briefing.” Republican aides in both chambers also insist Rice was not neglecting Democrats, and in fact was adamant about wanting to brief both parties to prevent the perception of partisanship.

Majority Leader Tom DeLay (R-Texas), responding to questions from House Minority Whip Steny Hoyer (D-Md.) about the topic on the floor Thursday, said the Rice sessions were not intended to close out the Democratic Members. DeLay noted that Rice offered to meet with Democrats, and that it is always the minority party’s prerogative to seek meetings with White House officials.

“No one is trying to be shut out, but there are times when our Caucus wants to talk to this administration and we ought to be allowed to do that as long as we get briefings and open briefings in a bipartisan way as well,” DeLay said.

Hoyer, however, argued that the Iraqi conflict is too important an issue, and called on DeLay to ensure that similar meetings are bipartisan in the future. Hoyer said it is critical Members receive the same information from the White House and can listen to both parties’ questions and concerns at the same time.

“We were disappointed that this briefing was given on partisan basis,” Hoyer said. “We do not think that is in the best interest of the country; we do not think it is in the best interest of this Congress.”

On the Senate side, Sen. Jon Corzine (D-N.J.), chairman of the Democratic Senatorial Campaign Committee, echoed those sentiments, saying “it would have been better” to have bipartisan meetings.

Senate and House Democratic aides indicated that in setting up the briefings, the White House contacted Senate Minority Leader Tom Daschle (S.D.) and House Minority Leader Nancy Pelosi (Calif.) late in the day Wednesday, making it difficult to schedule sessions with Rice difficult. House Democrats were unable to work Rice into their schedule last week and had to push their meeting until this week, while Senate Democrats were only able to pencil in the Rice meeting Thursday afternoon, sources said.

Paul Kane contributed to this report.