Immigration is an issue that Mr. Trump has repeatedly turned to as a way to shore up his political base whenever his fortunes have appeared troubled. In late 2018, as polls predicted — accurately, it turned out — deep Republican losses in the midterm elections, the president pointed to what he claimed was an “invasion” by a caravan of immigrants who were heading toward the southwestern border.

During Mr. Miller’s call, the acting deputy secretary for the Department of Homeland Security, Kenneth T. Cuccinelli II, echoed Mr. Miller’s comments by saying the president has been considering such a step “since the economic effects of the Covid virus began.”

Mr. Cuccinelli, a former Virginia attorney general who has long pushed for less immigration, told the president’s supporters on the call that “your best approach, in my view, is just to note this is a positive step — note the president has opened the door to more steps.”

“You can certainly expect more actions from him as time goes forward,” Mr. Cuccinelli added.

In response to a question from a caller about how to “message” the intent of the executive order, Mr. Cuccinelli said, “Talk about the fact that the president is taking steps, is taking this seriously, and has instructed us to prepare for other steps.”

The issue of what to do about legal immigration has long divided Republicans, and many in the president’s party on Capitol Hill oppose proposals that would block businesses — including technology companies in Silicon Valley and big agricultural industries — from tapping into large pools of foreign labor.

But others in the party, including Senator Tom Cotton of Arkansas, have repeatedly pushed for legislation that would reduce legal immigration. In 2017, Mr. Trump endorsed the RAISE Act, a bill that Mr. Cotton sponsored that would have cut legal immigration each year by about half, from about one million to about 500,000. The legislation ultimately went nowhere.

While Mr. Trump has often used immigration as a tool to rally his base, he has not been consistent in his approach. The administration is facing a potential inflection point when the Supreme Court rules in the next few months on whether the administration’s end of the program that protects undocumented immigrants who came to the United States as children, known as DACA, was done legally.