Senior White House adviser Stephen Miller Stephen MillerSpecial counsel investigating DeVos for potential Hatch Act violation: report Trump confirms another White House staffer tested positive for COVID-19 Biden pick creates furor, underscoring bitterness over Obama immigration policy MORE reportedly told supporters in an off-the-record call Thursday that President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's temporary order to suspend immigration is part of a larger strategy to reduce overall immigration.

According to audio of the call obtained by The Washington Post, Miller said that "the most important thing is to turn off the faucet of new immigrant labor" and that the temporary ban would limit "chains of follow-on migration."

Trump's order, signed Wednesday, suspended for 60 days the entry of some green card applicants based abroad.

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The order has carveouts for specific would-be immigrants, including essential workers, spouses and young children of U.S. citizens, investor visa beneficiaries and service members.

But no exclusions exist for foreign national parents and parents of U.S. citizens, spouses and children of legal permanent residents and beneficiaries of the diversity visa program, known as the visa lottery. Those groups have sometimes been referred to by the administration and immigration restrictionists as "chain migration."

Acting Deputy Homeland Security Secretary Ken Cuccinelli also joined the call and spoke briefly, according to The Post, saying that the order was in line with the administration's broader immigration policy.

“This is something the president has been looking at himself since the economic effects of the covid virus began,” Cuccinelli reportedly said. “We’ve had numerous conversations with him. And so what you saw yesterday was a continuation of his own thinking.”

Miller portrayed the order as a "historic" move to protect American workers from undue foreign competition.

After the executive order was announced, immigration advocates argued that it had all the markings of Miller's influence.

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"Stephen Miller somehow, someway convinces President Donald Trump to constantly go to immigration as an issue, regardless of the policy matter we're trying to address," Rep. Tony Cárdenas (D-Calif.) told The Hill on Friday.

The White House did not immediately respond to a request for comment.

Miller, who has long argued that immigration hurts American workers, has maintained close ties with groups that advocate for placing more restrictions on immigration.

Those groups blasted Trump's executive order for not including more restrictions, such as moratoriums on guest worker visas.

Roy Beck, president of NumbersUSA, said in a statement that "corporate lobbyists and other immigration expansionists in the White House persuaded the President to significantly water down" his order.

In a Fox News interview Thursday, acting Homeland Security Secretary Chad WolfChad WolfOvernight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers Senate to hold nomination hearing for Wolf next week Hillicon Valley: FBI chief says Russia is trying to interfere in election to undermine Biden | Treasury Dept. sanctions Iranian government-backed hackers MORE said his agency will soon recommend a move to limit temporary work visas as well.

"That is something that the department has been looking at for the past several months, so we are well underway and look forward to presenting to the President those recommendations for additional steps," said Wolf.

Updated: 6:25 p.m.