"Unfortunately, President Obama’s words today are not surprising since they follow upon various actions already taken by his Administration that erode or ignore the unique meaning of marriage," Dolan said in a written statement.
Dolan serves as the president of the U.S. Conference of Catholic Bishops.
Obama told an ABC News reporter today that he supported the redefinition of marriage.
“I’ve just concluded that for me personally it is important for me to go ahead and affirm that I think same-sex couples should be able to get married,”Obama said in an interview with ABC News’s Robin Roberts.
Obama's statement comes after Vice President Joe Biden on Sunday said he is "absolutely comfortable" with same-sex marriage, and Education Secretary Arne Duncan on Monday confirmed he also supports gay marriage.
Obama in February 2011 ordered the Justice Department to no longer defend the Defense of Marriage Act, which defines marriage as between one man and one woman. Later that year in September, the U.S. military ended its "don't ask, don't tell" policy.
Dolan noted he and the other U.S. bishops cannot stand by while a key societal principle is torn down.
"… We cannot be silent in the face of words or actions that would undermine the institution of marriage, the very cornerstone of our society. The people of this country, especially our children, deserve better," Dolan said.
Cardinal Francis George of Chicago told the Chicago Sun-Times Obama's statement veers from Church teaching.
"The Catholic Church teaches what she has received from the Lord," he told the Sun-Times. "Faithful Catholics hold that natural marriage is constituted in a relationship between a man and a woman whose mutual love is shared for life and for the sake of the family."
Bishop R. Daniel Conlon of Joliet later weighed in, issuing a statement in which he criticized Obama's use of the Golden Rule as stated in the Bible, saying, "the president justifies his position on marriage with an oversimplified interpretation of one verse of the New Testament, while ignoring the rest of the Bible on the subject of marriage, as well as three millennia of Judeo-Christian tradition."