"I do not favor civil unions if they are identical to marriage other than by name," he told the Fox TV station in Denver. "My view is the domestic partnership benefits, hospital visitation rights, and the like are appropriate but that the others are not."
The Romney campaign did not respond to requests for clarification about which benefits Romney supports and which he does not.
Romney also faced an internal issue this month when his openly gay national security spokesman, Richard Grenell, resigned after his support for gay marriage drew intense criticism from conservatives.
Grenell, who served as spokesman for then-U.N. Ambassador John Bolton during the Bush administration, said in a statement that Obama is on the "the right side of history," though he suggested the president is playing politics with civil rights.
A new Associated Press-GfK poll shows independent voters trust Obama over Romney to handle social issues "such as abortion and same-sex marriage," with 39 percent favoring Obama and 22 percent favoring Romney. A majority of voters trust Obama over Romney in every age group except senior citizens.
While conservative Republicans trust Romney over Obama by wide margins, moderate and liberal Republicans are almost evenly split between Obama and Romney.
Hunt reported from Washington. Associated Press Deputy Polling Director Jennifer Agiesta and Associated Press writer Steve LeBlanc in Boston contributed to this report.