WASHINGTON – The White House yesterday signaled it would back Senator Specter of Pennsylvania for the chairmanship of the Senate Judiciary Committee, despite calls for his ouster by social conservatives angered by his suggestion that he might not support anti-abortion judicial nominees.

President Bush’s chief political adviser, Karl Rove, said yesterday that the moderate Republican senator had assured the president he would bring all judicial nominees to a quick vote in the Senate.

“Senator Specter is a man of his word, and we’ll take him at his word if he becomes chairman of the Senate Judiciary Committee,” Mr. Rove said yesterday on the Fox News Channel’s “Fox News Sunday.”

Mr. Specter, who is next in line to assume the chairmanship of the committee according to Senate rules, has long been a target of social conservatives. He has said the Supreme Court opinion in Roe v. Wade upholding abortion rights is “inviolate.”

Last week, he cast doubt on whether he would support all of the president’s nominees, telling reporters, “That obviously depends upon the president’s judicial nominees. I’m hopeful that I can support them.”

He later qualified his comments, stating that he would bring all nominees to a quick vote in the Republican dominated Senate and would seek to prevent Democrats from holding up nominees using filibusters, which Republicans lack the votes to quash.

“The fact is that I have supported all of President Bush’s nominees in committee and on the floor. I have never applied a litmus test,” Mr. Specter said yesterday on CBS’s “Face the Nation.” “Although I am pro-choice, I have supported many pro-life nominees.”

Social conservative groups, who had opposed Mr. Specter in his close primary contest against the Rep. Pat Toomey, a conservative Republican Pennsylvania congressman, said Mr. Specter should not be allowed to take over the committee at a time when Chief Justice Rehnquist is ailing with thyroid cancer and several other aging judges could retire within the next four years.

The groups argue that given that the Christian social conservative base of the Republican Party turned out in record numbers to vote for preserving their moral values, the president has the “mandate” to appoint conservative judges.

The founder and chairman of an influential conservative group, Focus on the Family, James Dobson, yesterday called the senator “a big-time problem for us” who “stands in the roadway” of the “great mandate that has been given to the president now.” He said millions of people are upset over his comments.

Various groups organized a call-in campaign to members of the Senate to urge for Mr. Specter’s ouster. An anti-Specter Web site has been set up and petitions have been circulating.

“You couldn’t get a phone call into Washington, D.C., into the Capitol, on Friday because of these comments. And that’s not going to go away,” said Mr. Dobson, speaking on ABC News’s “This Week with George Stephanopoulos.”

Mr. Specter had “turned a blind eye to the very people who secured a second term for President Bush,” said Matthew Staver, the president and general counsel of Liberty Counsel, a conservative legal group.

“We need an advocate who can weather the battle over the next appointment to the U.S. Supreme Court,” he said in a statement on Friday.

Mr. Rove seemed to dismiss the concerns yesterday, stating that while “the senator is entitled to his opinions,” the president was satisfied that he would move the nominees along.

“Well, it was pretty straightforward and pretty plain. The president – he told the president, ‘I will make certain your nominees receive a hearing. I’ll make certain that they receive a vote, and the appellate nominees will be brought to the floor,'” Mr. Rove said.

Sean Rushton, the executive director of the Committee for Justice, a group that advocates for conservative judicial nominees, said yesterday that he saw “no sign” that Mr. Specter would be prevented from taking over the committee. Mr. Specter has a record of supporting Mr. Bush’s nominees to federal courts, and he convinced the White House and the Senate leadership of his loyalty prior to his primary run, Mr. Rushton said.

Mr. Specter was backed in the primary by Senator Santorum, the junior senator from Pennsylvania, a well-known social conservative.

With the election behind them, senators and the White House are less concerned about appeasing grassroots activists who failed to defeat Mr. Specter during the primary, Mr. Rushton said.

“The time to unseat him was in the primary, and the fact is, the whole establishment supported him and he eked out a victory,” he said.