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Last Wednesday, Stephen Moore, a scholar at the Heritage Foundation who is an outspoken supporter of an immigration overhaul, described a recent telephone call with Gov. Scott Walker of Wisconsin, in which he said Mr. Walker had assured him he had not completely renounced his earlier support for a pathway to citizenship for illegal immigrants.

“‘I’m not going nativist, I’m pro-immigration,’” Mr. Walker said, according to Mr. Moore’s account of the call to a reporter for The New York Times.

On Sunday, after three days of pressure from Mr. Walker’s aides, Mr. Moore said that he had “misspoken” when recounting his call with Mr. Walker — and that the call had never actually taken place.

The turnabout by Mr. Moore came after he was quoted Thursday in a Times article detailing Mr. Walker’s shifts on immigration, same-sex marriage and ethanol subsidies to protect his early lead in Iowa, where he is facing a well-financed challenge from Senator Ted Cruz of Texas, among other rivals.

Mr. Walker said in 2013 that he supported a pathway to citizenship for illegal immigrants. But he said in March that he had changed his mind, and now only backed stronger enforcement of the American border. Taking the more hawkish stance on immigration aligned him with some conservatives in the Republican primary electorate, notably in Iowa; it put him at odds with supporters of an immigration overhaul, who include Mr. Moore and a group he helps run, the Committee to Unleash Prosperity.

In the interview on Wednesday in which he had recounted Mr. Walker’s assurances that he was “not going nativist,” Mr. Moore said their conversation had occurred in “the last three or four weeks.” Asked if it had been in person or on the phone, Mr. Moore said: “I chatted with him on the phone.”

The article detailing Mr. Walker’s shifts in his positions, including Mr. Moore’s account of his conversation with the governor, was published online early Thursday morning.

Mr. Walker’s advisers contacted Mr. Moore about his comments in The Times article that afternoon, one of them said the following day. Walker aides were also apparently receiving inquiries from the conservative Breitbart News website, which on Friday night posted an article in which Mr. Moore recanted his account of the conversation with Mr. Walker.

But it was not until Sunday afternoon that Mr. Moore emailed this reporter to say he had “miscommunicated something to you in our interview.”

“The conversation that Scott Walker had on immigration wasn’t with me but one of the principals of our Committee to Unleash Prosperity,” Mr. Moore wrote. “In that conversation it became clear that as I said ‘he is not going in a nativist position on immigration.’ ”

Mr. Moore wrote that he had also personally talked to Mr. Walker about immigration in person earlier this year at a dinner put on by the committee, which is dedicated to promoting supply-side economics and a comprehensive immigration overhaul.

Setting aside the more recent phone call, Mr. Moore said he stood by his belief that Mr. Walker “was not going in a nativist direction on immigration.”

So, what exactly is Mr. Walker’s current position on immigration?

Asked if he supported any path to citizenship or legal status for illegal immigrants, Mr. Walker’s spokeswoman, AshLee Strong, did not directly respond. “The governor has made it clear that the immigration system is broken and we need to secure the border, enforce our laws, and have a legal immigration system in place that is good for the economy, working families, and wages,” she said in an email Monday. (In response to a query for the Thursday article about Mr. Moore’s conversation with Mr. Walker, Ms. Strong insisted that the governor was “not for amnesty.”)

This is the second time this year that Mr. Walker has been reported as saying privately that he was open to an immigration overhaul beyond measures to address the border, only to have his aides later deny such assertions were made.

In March, The Wall Street Journal reported that Mr. Walker said at a private dinner with New Hampshire Republicans that he was open to letting illegal immigrants eventually obtain American citizenship. Mr. Walker’s aides disputed that account as well.