The Carter administration yesterday continued its search for high-level appointees in the wake of last week's Cabinet purge as President Carter invited several hundred government employes to the White House to explain what the shakeup will mean to them.

With Carter's top priority finding a replacement for G. William Miller as chairman of the Federal Reserve Board, speculation centered on two possible successors: Bruce MacLaury, president of the Brookings Institution, the Washington-based research organization, and Paul Volcker, president of the New York Federal Reserve Bank.

Both men are considered more conservative than Miller, who has been nominated to succeed W. Michael Blumenthal, the ousted Treasury secretary.

Meanwhile, Carter resumed his routine duties yesterday, hosting a breakfast for congressional leaders at which he reportedly said he will nominate a mayor to be secretary of housing and urban development.

Former New Orleans mayor Moon Landrieu was the name most frequently mentioned to succeed Patricia Roberts Harris at HUD. Harris has been nominated to replace Health, Education and Welfare Secretary Joseph A. Califano Jr., who was fired by the president last week.

Others mentioned in the HUD speculation were Mayors Tom Bradley of Los Angeles and Richard Hatcher of Gary.

Carter must also find a replacement for Transportation Secretary Brock Adams, another victim of the purge. Several names figured in the speculation on Adams' successor, among them Massachusetts Lieutenant Governor Thomas P. O'Neil III, the son of House Speaker Thomas P. (Tip) O'Neil Jr. (D-Mass.), and Reps. James J. Howard (D-N. J.) and Norman Mineta (D-Calif.).

The president has promised prompt action in filling the high-level vacancies, particularly the Fed chairmanship. He has scheduled a news conference from the East Room of the White House at 9 tonight, at which time some appoinments could be announced.

White House press secretary Jody Powell said almost all of the congressional leadership breadfast was devoted to a discussion of the administration's energy proposals.

Powell said both he and Hamilton Jordan, the new White House chief of staff, attended the breakfast. Jordan, who has been criticized in the past by congressional leaders for unresponsiveness, is to have a larger role in dealing with Capitol Hill under the restructuring of the White House staff that is now under way.

Powell also announced that Carter will travel next Tuesday to Bardstown, Ky., where he will conduct a "townmeeting". The trip is expected to be the first in an increased travel schedule by the president, who has promised more direct contact with the American people, bypassing, in some instances, the Washington press corps.

The officials invited to the White House late yesterday afternoon were high-level political appointees whose performance is being scrutinized in a White House-ordered "performance evaluation".

Carter held a similar session Monday for the full White House staff, where he delivered a prep talk, telling his aides he expected competence and loyalty from them.