WASHINGTON — The Supreme Court on Tuesday seemed deeply divided about one of the great civil rights issues of the age: whether the Constitution guarantees same-sex couples the right to marry.

The justices appeared to clash over not only what is the right answer but also over how to reach it. The questioning illuminated their conflicting views on history, tradition, biology, constitutional interpretation, the democratic process and the role of the courts in prodding social change.

Justice Anthony M. Kennedy said he was concerned about changing a conception of marriage that has persisted for millennia. Later, though, he expressed qualms about excluding gay families from what he called a noble and sacred institution. Chief Justice John C. Roberts Jr. worried about shutting down a fast-moving societal debate.

In the initial questioning, which lasted about 90 minutes, Justice Samuel A. Alito Jr. asked whether groups of four people must be allowed to marry, while Justice Antonin Scalia said a ruling for same-sex marriage might require some members of the clergy to perform the ceremonies, even if they violate their religious teaching.

Source: Adam Liptak and Michael D. Shear, www.nytimes.com