Packer's comments have been criticized in the gay community as insensitive and hurtful to gay and lesbian Mormons.
Romney, as governor of Massachusetts from 2003 to 2007, presided over one of the few states in the nation that recognizes same-sex marriages. After the state's Supreme Court ruled a ban on gay marriage was unconstitutional, it was Romney who directed town clerks to begin issuing licenses to same-sex couples.
On Tuesday, the former governor expressed a sense that gays and lesbians should be entitled to basic rights, but reiterated his support for traditional marriage.
"I fully support the rights of gay individuals to choose their course in life, their careers in life, to have civil rights that are consistent with other citizens of the nation," Romney said. "As you know, I support traditional marriage. I believe that it is in the best interest of society, and at the same time I fully support the rights of gay individuals and homosexuals."
Running for president in 2008, Romney sought to put voters at ease with his Mormon faith, at one point making a major address about the role of religion in government. Ultimately he lost his party's nomination to Arizona Sen. John McCain.
Romney reiterated Tuesday that he has not decided whether he will challenge President Barack Obama for the presidency in 2012, although he is widely considered among the frontrunners if he should choose to run again.
He said he will decide with his family after the Nov. 2 election whether he will mount another campaign for the Republican nomination, or step aside and encourage others to run.
"Right now everything in our visibility is how to get good conservatives elected at the state level and at the national level," he said. "I fundamentally believe that this president and his fellow travelers in the leadership in Washington have put us on a very perilous course and we've got to get back to the values that make America's economy grow and protect our liberty and prosperity."
On Tuesday, Romney appeared at events in New Mexico, Arizona and Utah and was scheduled to head to Idaho on Tuesday night.