This story has been updated.

Likely GOP presidential candidate Scott Walker told a private gathering of New Hampshire business leaders earlier this month that he supports providing some illegal immigrants with a pathway to citizenship, according a person familiar with the discussion.

The position would mark a significant shift from away from the hardline "no amnesty" stance Walker has taken in public in recent weeks. The Wisconsin governor also told the small group that illegal immigrants seeking citizenship should not receive preferential treatment over applicants who are already in line, according to the person, who was not authorized to speak about it publicly.

The comments came at a March 13 dinner at the Copper Door restaurant in Bedford, N.H. The Wall Street Journal first reported Walker’s remarks, citing people who were there.

“He said no to citizenship now, but later they could get it,” Copper Door owner Bill Greiner told the Journal.

But a spokeswoman said the reports of Walker's remarks were false.  "We strongly dispute this account," Kirsten Kukowski said in a statement Thursday. " Governor Walker has been very clear that he does not support amnesty and believes that border security must be established and the rule of law must be followed. His position has not changed, he does not support citizenship for illegal immigrants, and this story line is false.”

The controversy comes as Walker prepares for a trip Friday to the U.S.-Mexico border in Texas as part of an attempt to bolster his conservative credentials on immigration issues. As he has risen to the top of several polls of Republican primary voters, Walker has shifted sharply away from past public support for a path to legalization to a stance against what he calls amnesty.

In a March 1 interview with Fox News, Walker said on immigration: “My view has changed, I’m flat-out saying it. Candidates can say that, sometimes they don’t.”

“I don’t believe in amnesty, and part of the reason that I made that a firm position is because I look at the way this president has mishandled that issue,” Walker added.

As a Milwaukee County executive a decade ago, Walker supported bipartisan efforts in Congress to enact comprehensive immigration reform.

But Walker's statements at the private dinner in New Hampshire, which will host the first 2016 presidential primary, underscores the difficulty of navigating the immigration debate for Republican contenders. Walker's chief rival in the polls, former Florida governor Jeb Bush, has long been supportive of a path to legalization for some immigrants as well as strengtehened border security. Walker's comments at the dinner echo much of what Bush has said in recent months on the campaign trail.

While many tea-party activists are opposed to a pathway to citizenship, the GOP's business wing and its powerful donors are mostly supportive. Walker's approach - moving right in his public rhetoric while reassuring others in private - reflects his broader attempt to win over both the hard-right and establishment blocs.

Many prominent conservative voices were already unsure of Walker's commitment to their "no amnesty" rallying cry even before his New Hampshire remarks were revealed. News of what he told business leaders may only fuel those suspicions.

"He has been on the same side as the progressive Left and the U.S. Chamber of Commerce Right: pro-amnesty, pro-massive legal immigration expansionist, and pro-Common Core," right-wing columnist Michelle Malkin told Breitbart News earlier this month. "He’s been left, right, center, and all over the map."

In a posting Thursday referring to Walker's immigration remarks on Fox News, RedState blogger Aaron Gardner asked, “Was it actually a change of heart, or a cynical attempt to placate those in the base? This sort of flip flopping on a controversial issue, after a national rollout that was less than impressive, cannot be good for the [governor’s] presidential aspirations.”

Walker's border trip is a part of a swing through the Lone Star State that will also take him to Houston on Saturday, where he will be the keynote speaker at the Harris County GOP’s Lincoln-Reagan dinner. Gov. Greg Abbott (R-Tex.) will be with Walker at the border Friday.

Abbott’s close friend, Sen. Ted Cruz (R-Tex.), a fierce critic of President Obama’s immigration policies, announced his 2016 campaign on Monday in an appearance at Liberty University in Lynchburg, Va.