ASHINGTON, Oct. 12 - Barely four months after dodging a ruling on the merits of the words "under God" in the Pledge of Allegiance, the Supreme Court agreed on Tuesday to examine another heavily freighted symbol of religion in public life: the Ten Commandments.

The justices accepted appeals from two opposing lower-court rulings, one that upheld the display of a six-foot-high Ten Commandments monument on the grounds of the Texas State Capitol and another that ordered two Kentucky counties to remove framed copies of the Commandments from their courthouse walls.

The two cases pose the question of whether the display of these images on government property amounts to an unconstitutional "establishment" of religion. The United States Court of Appeals for the Fifth Circuit, upholding the Texas monument in a ruling last November, said that the Ten Commandments convey "both a religious and secular message" and that "religion and government cannot be ruthlessly separated."

As a secular symbol, the appeals court said, the Commandments stand for "a regimen of just governance among free people," an acceptable image for placement in a public park between the state's legislative and supreme court buildings.

Almost simultaneously, the United States Court of Appeals for the Sixth Circuit ruled that McCreary and Pulaski Counties in Kentucky had to remove the Ten Commandments from their courthouse walls because the "predominant purpose for the displays was religious" despite being placed among such secular texts as the Declaration of Independence, the Mayflower Compact and proclamations by Presidents Abraham Lincoln and Ronald Reagan.

"The government must present the Ten Commandments objectively and must integrate them with a secular message," the appeals court said, concluding that the Kentucky counties had failed to do that.

Along with the Ten Commandments cases, the justices accepted a separate case on Tuesday on the degree to which the government may accommodate the religious needs of prison inmates, as required by a recently enacted federal law. The three cases mark the court's new term, just entering its second week, as potentially the most important in years for defining the ever-shifting boundary between church and state.

There is no way to read any particular message in the justices' decision to take up the Ten Commandments cases. With the lower courts in great disarray, and with new cases being filed around the country, the Supreme Court's intervention was not surprising.

The justices declined several times over the past year to get involved in the heated dispute in Alabama over the refusal by the state's chief justice, Roy S. Moore, to remove a 5,280-pound Ten Commandments monument from his courthouse on the order of a federal court. A special state ethics panel removed the chief justice from office for his defiance. One difference between the Moore case and the appeals the Supreme Court accepted is that Chief Justice Moore was waging a personal battle, while the displays the justices will review reflect official policy.

The Texas Legislature received the Ten Commandments monument in 1961 as a gift from the Fraternal Order of Eagles, an organization that placed thousands of such monuments on public property in the 1950's and 1960's. The organization said the Commandments offered a personal code of behavior that would reduce juvenile delinquency, a stated goal the Fifth Circuit opinion cited as evidence of a lack of religious purpose behind the display.

The Supreme Court has issued only one Ten Commandments decision, a two-page opinion it issued by a 5-to-4 vote in 1980 striking down a Kentucky law that required the posting of a copy of the Commandments in every public school classroom. "The Ten Commandments is undeniably a sacred text in the Jewish and Christian faiths, and no legislative recitation of a supposed secular purpose can blind us to that fact," the court said in that case, Stone v. Graham. Two justices who participated in that case remain on the court: Justice John Paul Stevens, who was in the majority, and Chief Justice William H. Rehnquist, then an associate justice, who voted in dissent.

There are several cases at the court now concerning displays of the Ten Commandments in the schools, including one from Harlan County, Ky., that the justices might have acted on but chose not to on Tuesday. As the court learned in its consideration of the Pledge of Allegiance case during the past term, the school environment presents a particularly thorny issue. R. Ted Cruz, the Texas solicitor general, referred in his brief in the Texas Ten Commandments case to "a potentially coercive schoolroom setting," which his case did not present.

Although Texas prevailed in the Fifth Circuit, Mr. Cruz urged the justices to hear the appeal brought by Thomas Van Orden, the original plaintiff, who argued his own case in the appeals court. He is now represented by Erwin Chemerinsky, a Duke University law professor. Mr. Cruz said the court should hear the appeal, Van Orden v. Perry, No. 03-1500, in order to affirm the lower court's opinion.

The American Civil Liberties Union brought the Kentucky courthouse cases on behalf of several local residents. The counties are being defended by Liberty Counsel, a public interest law firm in Longwood, Fla., that represents religious-right causes. Its appeal is McCreary County v. A.C.L.U. of Kentucky, No. 03-1693.

Last term's religious symbol case, a father's challenge to the recitation of the Pledge of Allegiance in his daughter's public school classroom, ended inconclusively in June when five justices decided that the father, Dr. Michael A. Newdow, lacked standing to pursue the case. Three other justices, Chief Justice Rehnquist and Justices Sandra Day O'Connor and Clarence Thomas, wrote separately to say that in their opinion, the insertion of "under God" in the Pledge 50 years ago did not make it unconstitutional. Justice Antonin Scalia shares that view; in fact, he recused himself from the case because he had expressed it publicly.

The other church-state case the court accepted Tuesday will provide its first examination of a four-year-old federal law, the Religious Land Use and Institutionalized Persons Act. Designed to replace the Religious Freedom Restoration Act, a broader law the court declared unconstitutional in 1997, this law requires the government to give special justification for any law that places a burden on a religious organization through land-use policies or on a prisoner through regulations.

The prisoners'-rights portion of the statute is at issue in the new case, Cutter v. Wilkinson, No. 03-9877. Five Ohio prison inmates, adherents of unconventional religions like Wicca and Asatru, invoked the law to protest denial of access to ceremonial items and opportunities for group worship. In an opinion last November, the Sixth Circuit declared that the law was an unconstitutional establishment of religion. Three other federal appeals courts, by contrast, have upheld it.

The implications of this case are considerably broader than either prisons or, by some accounts, the statute itself. "It's about whether government can pass any law that specially accommodates religious exercise," Anthony R. Picarello Jr., president and general counsel of the Becket Fund for Religious Liberty, said Tuesday. The fund has defended the law in dozens of cases around the country.