WASHINGTON, Nov. 9  The White House said today that it would seek Senate confirmation of Defense Secretary Donald H. Rumsfeld’s successor in the lame duck Congress that is about to reconvene, and that it would seek confirmation of United Nations Ambassador John R. Bolton as well.

Confirmation of Robert M. Gates to replace Mr. Rumsfeld and of Mr. Bolton, who was installed in the United Nations post under temporary status by President Bush, were two priorities cited by Tony Snow, the White House spokesman, on a day when Democrats flexed their new political muscle while exchanging conciliatory words with the president. Before having lunch with Democrats, Mr. Bush met with Senators Bill Frist of Tennessee, the retiring majority leader; Mitch McConnell of Kentucky, the Republican whip, and House Republican leaders, Mr. Snow said.

“The readout I got from the meeting is, it was primarily focused on the lame-duck session,” Mr. Snow said at a White House briefing. He ticked off a list of pending issues, which he said included “the nominations of John Bolton and also, if possible, Bob Gates.”

Shortly afterward, the White House officially announced one nomination: “John Robert Bolton, of Maryland, to be Representative of the United States of America to the Sessions of the General Assembly of the United Nations during his tenure of service as Representative of the United States of America to the United Nations.”