Supreme Court Chief Justice William H. Rehnquist (search) on Monday read aloud a ruling he had authored, but offered no news about his own plans, disappointing court watchers who had expected him to announce his retirement.

Even so, the 80-year-old justice may have presided over the nation's highest court for the final time. The court said no retirement announcement would come Monday, but a resignation, most likely in the form of a press release or a letter to the president, could come any day before the next Supreme Court session begins Oct. 3.

George Washington University law professor Jonathan Turley told FOX News that the court's adjournment for the summer did not rule out a retirement.

"Rehnquist could take the summer and see how his health improves and whether it does improve before he resigns," said Turley. "Indeed, if he resigned at the end of the summer it might be better for the White House, so you don't have a nominee dangling out there for months."

Mike Carvin, legal counsel for the Bush-Cheney campaign during the 2000 Florida recount, agreed that Monday's lack of retirement news meant little.

"I never expected him to [retire] from the bench this morning, so that doesn't tell you a lot," Carvin said.

Rehnquist has been battling thyroid cancer since last fall. Although he walked out of his Arlington, Va., home Monday morning aided only by a cane, many believe the justice, appointed to the court by President Richard M. Nixon in 1971, could be formulating his exit.

In court Monday, Rehnquist, slowed by a trachea tube inserted to help him breathe, cleared his throat several times as the court issued rulings on two significant cases regarding the Ten Commandments (search), as well as others concerning anonymous press sources and Internet file-sharing of movies and music.

Rehnquist read the second Ten Commandments ruling, which permitted a monument to the Biblical laws to stay on the grounds of the Texas Capitol.

He then thanked the court's employees for their work over the past year before adjourning the session.

While most retirement speculation has been on Rehnquist, Justice Sandra Day O'Connor (search), 75, could also step down soon. O'Connor, the first woman to become a Supreme Court justice, was appointed by President Ronald Reagan in 1981. There are reports she would like to retire to her home in Arizona.

Conservative and liberal political-action groups have been gearing up for a retirement for months, and the fight over any Supreme Court nomination by President Bush is expected to be fierce.

Still, C. Boyden Gray, White House counsel for President George H.W. Bush, said he did not expect a retirement to be timed to any reduction of tensions in the Senate.

"I think the more relevant factor is the 2006 election [and] what that means, the 2008 election [and] what that means," said Gray. "Will Republicans hold the White House after that? When does President Bush become a lame duck? I think that's far more relevant.

"The climate in the Senate turned better for Bush's nominations after the so-called deal" to limit judicial filibusters, Gray added, "so I don't think the climate is one affecting any of their decisions."

FOX News' Sharon Kehnemui Liss contributed to this report.