WASHINGTON - Sen. Bill Frist, the Republican majority leader, said Sunday that he was troubled by recent remarks by Sen. Arlen Specter, R-Pa., about potential judicial nominees, and that Specter must convince his fellow Republicans that he deserves to be chairman of the Senate Judiciary Committee.

''Arlen made some statements the day after the election,'' Frist, of Tennessee, said on ''Fox News Sunday'' in an interview with Chris Wallace. ''They were disheartening to me; they were disheartening to a lot of people.''

Specter said just after he won re-election that Supreme Court nominees who wanted to undo abortion rights would face tough confirmation fights in the Senate. Those remarks, in keeping with Specter's support of abortion rights and with his maverick personality, put him at odds with conservative Republicans and annoyed the White House.

Specter tried Sunday to ease the concerns of his party, saying in an interview with George Stephanopoulos on the ABC News program ''This Week'' that he had never required ''a litmus test'' for Supreme Court nominees.

Specter wants and is in line for the Judiciary post when Sen. Orrin Hatch of Utah steps down because of Republican rules limiting the terms of chairmen.

Frist pointedly declined to endorse Specter for the post on Sunday, saying that Specter should lobby his Republican colleagues in the Senate's lame-duck session this week.

Specter did pick up some support on Sunday. Sen. Richard Lugar, R-Ind., said he backed Specter - but mainly because of Senate rules. ''If Republicans decide they want to change of all them, that's a different situation,'' Lugar said in an interview with Wolf Blitzer on CNN.

Another Republican, Sen. John McCain of Arizona, said on ''This Week'' that he backed Specter without reservation. ''I believe that Arlen has done a good job,'' McCain said. ''I think he'll be confirmed.''