A Fox News poll released Thursday shows President Barack Obama leading Mitt Romney on gay marriage.

The national survey of 930 registered voters conducted between August 5 and 7 shows 54 percent of voters have a positive view of Obama. Four years ago, 59 percent of voters viewed him positively.

The Obama campaign in recent weeks has released several ads critical of Romney, the likely GOP presidential nominee, for refusing to release his tax returns.

Romney's favorable rating sits at 46 percent, down from 52 percent in mid-July.

“The events of the past two weeks appear to have energized Democratic voters a bit,” Republican pollster Daron Shaw said. “But perhaps more critically, Romney's support among independents has declined. The Obama campaign has – at least in the short-term – succeeded in raising questions about Romney's fitness to govern and in making this less of a referendum and more of a choice election.”

Respondents said they trusted Obama more than Romney on gay marriage, 52 percent to 32 percent.

The president announced his support for gay nuptials in May. He has also said he believes the Defense of Marriage Act (DOMA), which forbids federal agencies from recognizing the legal marriages of gay and lesbian couples, is unconstitutional.

Last year, Romney signed the National Organization for Marriage's (NOM) 5-point pledge promising to support a federal constitutional amendment banning gay marriage, defend the Defense of Marriage Act (DOMA) in court, appoint judges and an attorney general who will “respect the original meaning of the Constitution,” appoint a presidential commission to investigate the “harassment of traditional marriage supporters,” and back legislation that would allow a ballot question on the issue for voters in the District of Columbia.

(Related: Mitt Romney PAC donated to gay marriage foe NOM in 2008.)