GOP leaders are taking a closer look at newly re-elected Sen. Arlen Specter (search), who is set to head the Senate Judiciary Committee, after the Pennsylvania Republican made some seemingly stern warnings to President Bush Wednesday about his judicial nominees.

In a strategy phone call with Majority Leader Bill Frist (search) on Thursday, GOP leaders discussed in a "stern way" comments Specter made during a victory press conference following his election to a fifth term in the Senate.

At about the same time Bush was being declared the winner of the 2004 presidential election, Specter said he believed it is unlikely that the president might nominate abortion opponents to the Supreme Court, adding what sounded to some in the room like a subtle warning to the president.

"The president is well aware of what happened when a bunch of his nominees were sent up, with the filibuster," he said, referring to the success of Senate Democrats in the past four years to prevent the president's nominees from being confirmed to the bench. "And I would expect the president to be mindful of the considerations which I am mentioning."

Adding that the current Supreme Court lacks legal "giants" on the bench, Specter said the president would want to avoid nominating anyone who would oppose the 1973 decision legalizing abortion.

"When you talk about judges who would change the right of a woman to choose, overturn Roe v. Wade, I think that is unlikely," he said.

President Bush could have the opportunity to nominate judges to fill up to three vacancies to the nation's highest court. Four of the current justices are over age 70, and Chief Justice William Rehnquist, 80, has been facing a slower recovery than expected after a recent bout with thyroid cancer.

During his first press conference since April, Bush on Thursday brushed off questions on the topic.

"There's no vacancy on the Supreme Court. I'll deal with a vacancy when there is one."

But, he added, a look at his record of previous nominees should give an indication of the choices he would make.

"I told the people on the campaign trail that I'll pick somebody who knows the difference between personal opinion and the strict interpretation of the law ... and if people are interested in knowing the kind of judges I'll pick, look at the record," Bush said.

But while Republicans have made gains in the Senate to a 55-44-1 majority, the president still is not past the 60-vote threshold Republicans need to avoid a filibuster of his candidates.

"As it stands today [Democrats] can block [a nominee]," said C. Boyden Gray, former legal counsel to President George H.W. Bush. But I also believe that the president and majority leader may well decide to change the rules given the elections ... The president has a very strong political support, potential support, for asking for and getting this change."

Senate Democrats have managed in the past to stop six of the president's nominees to the federal bench, but Republicans pleased with their numbers on Tuesday said they may consider bringing back some of those candidates.

"I would like to see the president re-nominate a lot of these judges and let's get to them right away," said Virginia GOP Sen. George Allen.

"I'm very confident that now we've gone from 51 seats to 55 seats, we will be able to overturn what has become customary filibuster of judicial nominees," Frist said Wednesday in Orlando, Fla.

Specter is a loyal Republican and was endorsed by the president in a tight Pennsylvania GOP primary. He won re-election Tuesday with an 11-point margin, winning over many ticket-splitting Democrats in a state that went for John Kerry.

Specter is also known as someone willing to cross party lines to pass legislation and previously helped kill President Reagan's nomination of Robert Bork to the Supreme Court and of Jeff Sessions to a federal judgeship. Specter called both nominees too extreme on civil rights issues. Sessions later became a Republican senator from Alabama and now sits on the Judiciary Committee with Specter.

Specter has said he would characterize himself "as moderate; I'm in the political swim. I would look for justices who would interpret the Constitution ... reflecting the values of the people."

Republican leaders in the conference call Thursday said they wanted Specter to "issue a clarification" since his remarks upset several Republicans. A short time later, Specter did just that.

"Contrary to press accounts, I did not warn the president about anything and was very respectful of his constitutional authority on the appointment of federal judges," Specter said in a statement. "As the record shows, I have supported every one of President Bush's nominees in the Judiciary Committee and on the Senate floor. I have never and would never apply any litmus test on the abortion issue and, as the record shows, I have voted to confirm Chief Justice Rehnquist, Justice O'Connor and Justice Kennedy and led the fight to confirm Justice Thomas."

Specter added that he is interested in adopting a protocol for judicial nominees that would speed up the confirmation process and prevent filibusters.

It would be difficult and unusual to deny Specter the chairmanship based on his earlier comments, but not impossible. The Philadelphia senator must have the support of his fellow Republicans on the committee in order to gain the post. Six of the committee's 10 Republicans, including Sessions, can be considered very conservative.

FOX News' Brian Wilson and Molly Hooper and The Associated Press contributed to this report.