Some of the nation’s most influential evangelical groups urged a solution to illegal immigration Tuesday that defies the harsh rhetoric of the Republican primary race, which continues to undermine Mitt Romney’s appeal to Hispanic voters.

The call by the groups represents a recognition that in one bedrock element of the conservative movement — evangelical Christians — the demography of their followers is changing, becoming more Hispanic, and Republican leaders risk being out of step with their hawkish talk of border fences and immigration crackdowns like those in Arizona.

Tom Minnery, the senior vice president of policy for one evangelical group, Focus on the Family, said many of the 11 to 12 million illegal immigrants should be free to “come out of the shadows” and “begin the process of restitution” leading to attaining legal residency.

He spoke at a Capitol Hill news conference called to announce that more than 150 Christian evangelical leaders, including from the Southern Baptist Convention and the National Association of Evangelicals, were endorsing immigration overhaul.

The evangelical leaders expressed opposition to such notions as “self-deportation,” which Romney favored in a Republican debate and which urges strict enforcement of laws to encourage illegal immigrant workers to leave the country.

The situation is considered all the more critical given that some key swing states in the coming election — including Colorado, Nevada and Florida — have large Hispanic populations that leading Republicans say they must win over to prevail in these states.

“This is the tipping point to finally convince Republican operatives that they must redeem the narrative on immigration reform in order to be a viable party in America’s political landscape in the 21st century,” said Samuel Rodriguez, president of the National Hispanic Christian Leadership Conference.

Rodriguez said he met last week with aides to Romney to urge the presumptive Republican nominee to moderate his positions.

He noted that Hispanics, who account for about 7.5 million of the 82 million evangelicals in the country, are the fastest-growing segment. Hispanic evangelicals are more likely than other Hispanics to identify as conservative and Republican.

But so far Romney has shown no inclination to shift his positions from the primary season, when he attacked rivals Newt Gingrich and Gov. Rick Perry of Texas for their more moderate immigration stances.

Although he has campaigned with Sen. Marco Rubio of Florida, a Cuban-American popular with the Tea Party, Romney has not endorsed Rubio’s proposal to grant a path to legal residency for some children of illegal immigrants. He plans to address a national meeting of elected Hispanic officials June 21 in Orlando, Fla., and is expected to speak about immigration.

For now, Romney’s strategists argue that he need not change his positions because Latino voters will cast ballots in November based on the economy, not immigration.

One recent poll in Florida suggested a tightening of the race among the large Latino population there. A Quinnipiac poll in late May had President Barack Obama’s support at 42 percent of Hispanic registered voters and Romney at 40.

“Gov. Romney believes that legal immigration is a source of strength for America and that to protect legal immigration we must address illegal immigration in a civil but resolute manner,” said Alberto Martinez, an adviser to Romney in Florida. “As president, Gov. Romney would work with any groups on a reform that strengthens legal immigration, secures our borders, respects those who are waiting patiently to enter legally and ensures that we do not encourage further illegal immigration.”

A pro-reform movement has been percolating among evangelical groups for the past two to three years, with organizations and churches that align with Republicans on issues like abortion and gay marriage supporting Obama on immigration reform.

The National Association of Evangelicals, which represents more than 40 denominations, passed a resolution calling for comprehensive immigration overhaul in 2009. The Southern Baptist Convention did so last year.

It called for “just, fair immigration reform,” said Richard Land, president of the Southern Baptists’ ethics commission, who also attended Tuesday’s news conference.

“It passed with at least an 80 percent vote,” he said, “and four of five Southern Baptists is about as good as you’re going to get on any given day on anything.”

But Focus on the Family, the radio ministry based in Colorado, was a newcomer to the cause of immigration overhaul. While some advocates favor a path to citizenship for many illegal immigrants, Minnery of Focus on the Family advocated only a path to legal status, such as a work visa, after a fine is paid.

“These are the victims of economic misery so there’s compassion necessary,” Minnery said. “But making restitution is a first step.”

“I think the people are in a different spot than the politicians are on this issue,” he added. “I think people are tired of the rhetoric and looking for some improvement in the immigration system.”

If illegal immigrants are going to be asked to get in line for legal status, first “you have to get the lines moving,” he said.

© 2012 The New York Times Company