Officials are hoping that by centering the reprieve program on American citizens and legal residents, they will blunt some Republican opposition. Americans cannot be deported from their own country, and deportations of their parents have left many children stranded here, often with serious consequences for their social progress.

The White House is also considering expanding a program Mr. Obama started in 2012, called Deferred Action for Childhood Arrivals, or DACA, which has given similar reprieves to nearly 600,000 young immigrants who came here as children. More than 700,000 additional young people could become eligible. Officials may also include the parents of immigrants with DACA deferrals in the new programs.

White House officials have declined to comment about the plans. They say no final decisions have been made on the scope of the programs or whether they will be announced this week or in December.

Mr. Obama’s actions will not make it easier for migrants to cross the southwestern border, like the thousands of youths without their parents who floated on rafts across the Rio Grande into South Texas over the summer. Foreigners caught at the border would still be on the priority list for deportation, administration officials said, and a primary goal of Mr. Obama’s actions will be to shift resources and agents to border security that had been focused on removing immigrants from the interior.

Administration lawyers said they were preparing their case that enacting such measures would be within Mr. Obama’s constitutional authority. They cited the president’s wide latitude in enforcing the nation’s immigration laws.

Congress has provided only enough funding for the administration to carry out about 400,000 deportations each year. Mr. Obama, to the dismay of immigrant-rights advocates, has met that goal, removing more than two million immigrants while in office. But with 11.3 million people in the United States illegally, the lawyers’ argument goes, enforcement agents will never be able to deport them all. The president, officials say, has to devise policies that allow enforcement agents to go after convicted criminals and others who pose serious threats to public safety and national security.