John Kelly told a private meeting of Hispanic members of Congress that "certain things are said during the campaign that are uninformed".
The Post said its report is based on notes from two congressmen who were in the room during the meeting and confirmed by two other lawmakers and a senior aide who were also present.
John Kelly's comments come amid a shaky effort to reach a deal to protect hundreds of thousands of young immigrants from deportation.More news: 3 law enforcement officers shot overnight in York County, officials say
Gutiérrez also went on to confirm reporting by The New York Times that Kelly took credit as the " Trump's more extreme opinions on the wall and the viability of the Deferred Action for Childhood Arrivals initiative, also known as DACA. Last September, Trump announced he would end the program in six months if Congress could not pass immigration reform to replace it.
On Fox News Wednesday, Kelly reportedly explained, "We have some ideas on things like visa fees, renegotiation of NAFTA ... but not directly from their government".
As recently as Sunday, Trump was far more pessimistic about the program's future and criticised its Democratic supporters.
Kelly told lawmakers that "he was the one who tempered" Trump "on the issue of the wall, on the issue of DACA", said Representative Raúl Grijalva, a Democrat from Arizona, who attended the session. He reportedly told the group that "a concrete wall from sea to shining sea" wouldn't be built, but would instead be a "physical barrier in many places".More news: Arun Mishra pulls out of Loya case
Kelly says in an interview with Baier that "there's been an evolutionary process that this president's gone through" on issues ranging from Afghanistan to his promised Southern border wall.
Trump often cited his promise to build a "big, handsome wall" to energise his campaign rallies.
Luis Gutierrez, a Democratic congressman, said the caucus' meeting with Kelly was positive but he offered no solution to the immigration standoff. But he did not dispute the notion that the president has changed his view of what is needed to secure the border, based in part on information from Customs and Border Protection, the government agency charged with immigration enforcement.
Kelly added that the USA can explore end arounds for wall funding.More news: Why crude oil prices are on upward swing, by USA energy agency
According to the Post, Kelly "talked to Trump to tell him that the proposal would probably not be good for his agenda", adding that Kelly has provided Trump with major input on immigration following his brief stint as secretary of Homeland Security.
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