The new president of the Human Rights Campaign lauded the development.
"President Obama's words today will be celebrated by generations to come," Chad Griffin said in a statement.
Griffin later told CNN's "Piers Morgan Tonight" that "we will never have another president, Democrat or Republican, that opposes gay marriage."
Same-sex marriage foe Bill Donohue, president of the Catholic League, told Morgan that "a child needs a mother and father."
Barney Frank, a gay Democratic congressman from Massachusetts, appearing on CNN's "Erin Burnett OutFront," said that "no president could have done this 10 years ago."
Obama's interview followed recent comments by other key administration figures.
Vice President Joe Biden said Sunday on NBC he was "absolutely comfortable" with couples of the same gender marrying, leading observers to wonder when Obama would again address the issue.
Education Secretary Arne Duncan on Monday also made headlines when he openly backed same-sex marriage rights. Asked on MSNBC's "Morning Joe" if he supports allowing individuals of the same gender to legally wed, Duncan replied: "Yes, I do."
Before Tuesday, 30 states had voted in favor of constitutional amendments that seek to defend traditional definitions of marriage as a heterosexual union.
Massachusetts, Connecticut, Iowa, Vermont, New Hampshire, New York and the District of Columbia issue marriage licenses to same-sex couples.
In February, Washington Gov. Christine Gregoire signed a bill that would legalize same-sex marriage beginning in June, but opponents there have pledged to block the bill and called for voters to decide the issue.
Maryland Gov. Martin O'Malley signed into law a bill that permits the state's same-sex couples to wed as of January 1, and state residents may vote to affirm such a law. Minnesota will vote on a state constitutional amendment similar to the one in North Carolina. Maine will have a referendum on allowing same-sex marriage.
In 2011, the Pentagon stopped enforcement of the "don't ask, don't tell" policy on homosexuals serving in the military. That change played a part in Obama's announced stance on same-sex marriage.
"When I think about those soldiers or airmen or Marines or sailors who are out there fighting on my behalf and yet feel constrained, even now that 'don't ask, don't tell' is gone, because they are not able to commit themselves in a marriage, at a certain point 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," he told ABC News.
Legal challenges over same-sex marriage could reach the U.S. Supreme Court in coming months, but it seems unlikely justices would hear arguments before Election Day 2012.
The issue is on two legal tracks.
The Ninth Circuit U.S. Court of Appeals will decide the constitutionality of California Proposition 8, a voter-approved measure that would recognize marriage only between one man and one woman. A federal judge earlier struck down the law as a violation of equal protection, prompting the current appeal.
The Obama administration announced last year it believed the Defense of Marriage Act, often referred to as DOMA, to be unconstitutional. The law defines marriage for federal purposes as unions only between a man and woman.
A federal appeals court in Boston last month heard a DOMA lawsuit by a same-sex couple in Massachusetts. At issue is whether the federal government can deny tax, health and pension benefits to same-sex couples in states where they can marry.
That federal law is being officially defended in court by House Republicans, led by Speaker John Boehner, R-Ohio, who stepped in after the Justice Department refused to participate.