"I think that's a healthy process and a healthy debate," Obama told ABC News' Robin Roberts in an exclusive interview on "Good Morning America."
Speaking just one day after voters in North Carolina approved a constitutional ban on same-sex marriage and civil unions, the president, who had opposed the ballot measure, conceded the outcome in the critical swing state was reasonable.
"This debate is taking place at a local level," he said. "And I think the whole country is evolving and changing. And, you know, one of the things that I'd like to see is that a conversation continue in a respectful way."
Thirty states now have constitutional amendments or statutes banning same-sex marriage. Six states plus the District of Columbia have legalized the unions. The issue will be put directly to voters in Minnesota, Maine, Washington and Maryland in November.
Eager not to alienate key swing voters, Obama also reached out directly to same-sex opponents, telling Roberts that many Americans who disagree with him "are not coming at it from a mean-spirited perspective."
"They're coming at it because they care about families," he said. "And they have a different understanding, in terms of, you know, what the word 'marriage' should mean. And a bunch of them are friends of mine, you know, pastors and ... people who I deeply respect."
As for his personal evolution on the issue, Obama cited New York state, which approved gay marriage in June 2011, as an example of how compromise could be reached with religious groups, many of which oppose same-sex unions.
"I asked myself right after that New York vote took place, if I had been a state senator, which I was for a time, how would I have voted?" Obama told Roberts. "And I had to admit to myself, 'You know what? I think that I would have voted yes.'
"It would have been hard for me, knowing all the friends and family that are gays or lesbians, that for me to say to them, you know, 'I voted to oppose you having the same kind of rights and responsibilities that I have,'" he said.
Obama added that his shift on the issue came through conversations with staff members, openly gay and lesbian service members and his wife and daughters.
"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 said.
"The winds of change are happening. They're not blowing with the same force in every state," he added. "I think that as more and more folks think about it, they're gonna say, you know, 'That's not who we are.'"
Obama had been moving in the direction of supporting same-sex marriage since taking office in 2009 but has consistently stopped short of backing it outright. His announcement just six months from Election Day could have an electoral impact.
Obama has always stressed support for civil unions for gay and lesbian couples that provide the rights and benefits enjoyed by married couples, although not defined as "marriage," and opposed efforts to ban gay marriage at the state level, saying that he did not favor attempts to strip rights away from gay and lesbian couples.
But the president's position became a flashpoint this week when Vice President Joe Biden pronounced himself "absolutely comfortable" with allowing same-sex couples to wed.
Obama aides insisted there was no daylight between the positions held by the president and his vice president when it comes to legal rights, but as other prominent Democrats also weighed in favor of gay marriage, the disconnect became difficult for the White House to explain away.
"I've been consistent in my overall trajectory. The one thing that I've wrestled with is this gay marriage issue," Obama told Roberts when asked about the timing of his announcement. "And I think it'd be hard to argue that somehow this is something that I'd be doing for political advantage because, frankly, you know, the politics, it's not clear how they cut."
Polls show most Americans under the age of 40 support same-sex marriage -- a 61 to 35 percent margin in the latest ABC News/Washington Post poll. But most over the age of 65 -- 54 percent -- oppose it.
A racial gap persists, as well, with majorities of whites and Hispanics favoring same-sex unions while blacks are largely opposed, 55 to 41 percent.
"In some places that are going to be pretty important on this electoral map it may hurt me," Obama said. "But, you know, I think it was important for me, given how much attention this issue was getting both here in Washington, but [also] elsewhere, for me to go ahead, 'Let's be clear: Here's what I believe.'"
The announcement completed a turnabout for the president, who has opposed gay marriage throughout his career in national politics. In 1996, as a state Senate candidate, he indicated support for gay marriage in a questionnaire, but Obama aides later disavowed it and said it did not reflect the candidate's position.
In 2004, as a candidate for the U.S. Senate, he cited his own religion in framing his views.
"I'm a Christian," he said. "I do believe that tradition and my religious beliefs say that marriage is something sanctified between a man and a woman."
He maintained that position through his 2008 presidential campaign and through his term as president, until today.
As president in 2010, Obama told ABC News' Jake Tapper that his feelings about gay marriage were "constantly evolving. I struggle with this."
A year later, the president told ABC's George Stephanopoulos, "I'm still working on it."
"I probably won't make news right now, George," Obama said in October 2011. "But I think that there's no doubt that as I see friends, families, children of gay couples who are thriving, you know, that has an impact on how I think about these issues."
Obama's decision has political connotations for the fall. The issue divides elements of the Democratic base, with liberals and gay-rights groups eager to see the president go further, but with gay marriage far less popular among African-American voters.
Obama's likely Republican opponent, Mitt Romney, opposes gay marriage and fought his state's highest court, as governor, when Massachusetts became the first state to legalize gay marriage in 2004. Romney said on the campaign trail Monday that he continues to oppose gay marriage.
"My view is that marriage is a relationship between a man and a woman," Romney said. "That's the position I've had for some time, and I don't intend to make any adjustments at this point ... or ever, by the way."
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