OKLAHOMA CITY — Down the road from the Oklahoma State Capitol, where a towering oil derrick on the grounds is a tangible reminder of the industry’s clout in the state, Mitt Romney took the podium at the state GOP headquarters Wednesday afternoon intent on hammering President Obama on his handling of the economy and domestic energy production.

Instead, the focus of the event became the GOP front-runner’s response to Obama’s change of position less than an hour earlier on the issue of same-sex marriage.

“I have the same view on marriage that I had when I was governor and that I’ve expressed many times,” Romney told reporters during a brief question-and-answer session after his 10-minute prepared remarks. “I believe that marriage is a relationship between a man and a woman.”

View Photo Gallery: With the Republican presidential nomination essentially assured, former Massachusetts governor Mitt Romney steps up his criticism of President Obama.

Romney had just delivered remarks to some four dozen members of the party faithful in a state where, as Gov. Mary Fallin (R) noted shortly before Romney spoke, Sen. John McCain (R-Ariz.) won every county four years ago.

(Romney’s response to that observation: “Congratulations.”)

But the presumptive GOP nominee took pains to avoid a partisan tone in his response to questions about same-sex marriage, acknowledging that “this is a very tender and sensitive topic, as are many social issues.”

Asked whether he believed Obama had changed positions on same-sex marriage, Romney said it appeared that he had, although he added, “I guess you’ll be able to make that determination on your own.”

He added that decisions on domestic partnership benefits should be left up to the states.

Romney’s apparent choice not to use Obama’s same-sex marriage shift against him — at least, not at this early stage of the campaign — is the latest signal that the GOP intends to keep jobs and the economy front and center in the campaign.

It’s also a tacit acknowledgment that the issue can cut both ways, for both candidates.

Obama’s embrace of same-sex marriage rights Wednesday will almost certainly boost enthusiasm among the Democratic base.

At the same time, it comes at the risk of a downtick of support among older voters and more socially conservative Democrats, constituencies that stand to play a key role in swing states such as Florida, Ohio and North Carolina, which on Tuesday approved a measure banning same-sex unions.

Romney backs a constitutional amendment defining marriage as between a man and a woman and supports the Defense if Marriage Act, the 1996 law banning federal recognition of same-sex marriage.

But some Democratic critics argue that earlier in his career, Romney pledged to focus on expanding gay rights and point out that when same-sex marriage was legalized in Massachusetts in 2003, Romney initially said that the state should “follow the law” while also pursuing a constitutional amendment against gay marriage.

Some at Romney’s Oklahoma City event said they saw political peril for Obama in embracing same-sex marriage.

“I think the citizens of every state, I would think, would like in general to be able to govern themselves to the extent possible, for what’s appropriate in their area,” said Keith Peters, a 32-year-old attorney. “And to the extent that the president is not consistent on that, I think that does present a problem.”

Other attendees said they were unsure how the issue would play out.

The Wednesday event at Oklahoma GOP headquarters represented the second time in the past month that Romney has held an impromptu Q-and-A session with reporters in order to respond to Obama on the news of the day.

Last month outside Philadelphia, Romney and Sen. Marco Rubio (R-Fla.) held a joint news conference at which Romney announced that he supports extending federal student-loan rates at their current levels. Before that event, the last such news conference came in March, during the GOP primary in Puerto Rico.

In his prepared remarks Wednesday, Romney took note of the state’s 5.4 unemployment rate, which is well below the national average, and criticized Obama as a president who is “harking back to the old policies of the liberal past.”

Fallin, a former congresswoman who was elected governor in 2010, delivered a 10-minute introduction in which she hailed Romney as someone who can turn around the economy.

She noted that 300,000 jobs in Oklahoma are related to the oil and gas industry and described Obama as a president who “has been hostile to American-created energy” and who “didn’t have the courage to approve the Keystone pipeline.”

Romney, she argued, would be more of a partner as president.

“He won’t establish a government that’s kind of like our boss,” she told the crowd.

View Photo Gallery: President Obama endorsed same-sex marriage Wednesday, making him the latest — and most prominent — U.S. politician to call for gay nuptials. Here are a few other prominent political figures who have supported gay marriage.