The paper reported that Mr. Trump favoured immigrants from Norway and Asia, saying they help the country economically.
Trump said he is "ready and willing to make a deal" on the Deferred Action for Childhood Arrivals program, but he doesn't believe Democrats want to reach an agreement.
The debate over immigration policy became increasingly acrimonious after it was reported on Thursday that the Republican president used the word "shithole" to describe Haiti and African countries in a private meeting with lawmakers.
The former President of Ghana, John Dramani Mahama, who stepped down previous year, has also called on African presidents to condemn Trump's utterances.
On Sunday, the president defended himself in the wake of recent disparaging comments about Haiti and African nations, declaring that "I am not a racist". "I am the least racist person you have ever interviewed, that I can tell you".
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"The president has the right to make whatever remarks he wants and we respect the president", Goldstein told the broadcaster. "We can not let this derail us".
Trump's allies have argued that the controversy over his remarks is overblown.
The US president reacted to the outcry on Friday morning with a twisted denial on Twitter: "The language used by me at the DACA meeting was tough, but this was not the language used. Least racist person". @realDonaldTrump tonight to WH pool in comments as he entered dinner. Congress is grappling with the issue as they negotiate over a spending bill they need to pass by Friday to avoid a government shutdown. Some Democrats have called for a "clean" bill that addresses only the DACA issue.
Emotions are running high in El Salvador, Honduras and Nicaragua as Trump's administration moves to cancel temporary protection given to tens of thousands of their compatriots in the US. The president's inflammatory comments left lawmakers struggling to find a path forward. "We are responsible for who we are and how we behave", Love said.
After fellow Republican Senators Tom Cotton and David Perdue, who initially said they did not "recall" what the president had said, later outright denied that Trump had made the comments, Graham came close to calling them liars, saying that his "memory hasn't evolved" about the meeting. He called the new stories a "gross misrepresentation".
Al Jazeera's Kimberly Halkett, reporting from Washington, DC, said: "The calls for the president to apologise for his remarks are intensifying inside and outside the USA, but for now, that apology does not appear likely".