On Easter Sunday, weeks after he helped elect a new pope for a church struggling with declining numbers and controversy over social issues, Cardinal Timothy M. Dolan said that the Roman Catholic Church could be more welcoming of gay men and lesbians despite opposing same-sex marriage.

In recorded interviews with George Stephanopoulos on the ABC News program “This Week” and Bob Schieffer on “Face the Nation” on CBS, Cardinal Dolan, the archbishop of New York and one of the leading voices of the Catholic Church in the United States, did not suggest any changes in church teaching. He defined marriage as “one man, one woman, forever, to bring about new life,” but, he told Mr. Stephanopoulos, “we’ve got to do better to see that our defense of marriage is not reduced to an attack on gay people.”

“And I admit, we haven’t been too good at that,” the cardinal continued. “We try our darnedest to make sure we’re not an anti-anybody.”

Speaking just days after the Supreme Court heard arguments in two same-sex marriage cases, Mr. Stephanopoulos asked Cardinal Dolan what he could say to gay men and lesbians who felt excluded from the church.