Republican White House challenger Mitt Romney, wooing social conservatives, adamantly rejected same-sex marriage on Saturday and trumpeted his belief in Christian values and the family.

Three days after Barack Obama became the first US president to approve gay and lesbian marriage, Romney told university graduates that the 'pre-eminence of the family' remains at the heart of the principles that underpin the nation.

"As fundamental as these principles are, they may become topics of democratic debate," the presumptive Republican nominee told the class of 2012 at Liberty University, the biggest Christian campus in the United States.

"So it is today with the enduring institution of marriage. Marriage is a relationship between one man and one woman," he said, raising a loud cheer from a crowd of more than 25,000 -- the biggest so far in this campaign season.

Romney, who did not directly refer to gays or lesbians, had previously voiced opposition to gay marriage, although he has also stated same-sex couples should have some rights such as child adoption.

But Saturday's speech was his unbowed rebuttal in a week dominated by Obama's landmark endorsement of gay marriage, and the Republican hopeful sought to set himself apart from the president in the run up to November's election.

"Central to America's rise to global leadership is our Judeo-Christian tradition, with its vision of the goodness and possibilities of every life," he said in a speech punctuated with references to God.

"Take those away, or take them for granted, and so many things can go wrong in a life. Keep them strong, and so many things will go right."

Romney, a former governor of Massachusetts and venture capitalist with a personal fortune estimated at more than $250 million, also moved to rebut his image among some voters as a corporate suit who puts profit before people.

"I have never once regretted missing a business opportunity so that I could be with my children and grandchildren," he said, while also referring to his wife Ann, a homemaker who is often by his side on the campaign trail.

"Among the things in life that can be put off, being there when it matters most isn't one of them," he said, while seeking to tap into a sense among many evangelicals and the Catholic church establishment that Obama is riding roughshod over the constitutionally guaranteed freedom of religion.

"It strikes me as odd that the free exercise of religious faith is sometimes treated as a problem, something America is stuck with instead of blessed with," said Romney, a Mormon.

"Perhaps religious conscience upsets the designs of those who feel that the highest wisdom and authority comes from government -- but from the beginning, this nation trusted in God, not man," he said.

Virginia is a key battleground in the November 6 presidential election.

First Lady Michelle Obama beat Romney to the punch by delivering her own commencement speech at Virginia Tech university, about 90 miles (145 kilometers) from Lynchburg.

Romney was introduced to the stadium crowd -- 6,000 of whom were graduates -- by Liberty University president Jerry Falwell Jr, the son and namesake of its late Baptist founder, as "the next president of the United States."

On the struggling US economy, with unemployment still at 8.1 per cent, Romney told the young graduates: "If we take the right course, we will see a resurgence in the American economy that will surprise the world."

Liberty, the largest evangelical university in the world, is something of an essential campaign stop for Republican presidential candidates, having previously hosted Ronald Reagan and the elder George Bush.

But its invitation to Romney stirred controversy among some evangelicals due to his Mormon background and while Liberty students agreed with his opposition to same-sex marriage they urged him to apply caution.

"I thought the speech was great. A lot of things that he said, I agree on," said student Lindsay Burnett, noting that though she shares Romney's view on same-sex marriage, "on the other hand we're not here to judge others."

Many core Republicans remain wary of Romney, with critics saying he is a moderate who has suspiciously shifted his stance on social issues, including abortion.

Last year, pastor Robert Jeffress, a leader of the Southern Baptist Convention, the largest evangelical movement in the United States, dismissed Mormonism as "a theological cult."

But a new poll by Religious News Survey shows that such doubts about Romney might be waning among some core conservatives, with the presumptive Republican nominee enjoying a huge 68-19 per cent lead over Obama among white evangelicals.