In September, Mr. Trump ended an Obama-era program, called Deferred Action for Childhood Arrivals, or DACA, saying it was an illegal assertion of executive authority by his predecessor. But even as Mr. Trump’s actions threatened nearly 700,000 young immigrants with deportation when the program expires March 5, he has urged Congress to find a permanent solution that could allow them to live and work in the country legally.

In addition to suggesting a pathway to citizenship for the Dreamers, Mr. Trump said that he would request $25 billion to build a wall along the United States border with Mexico, though he said he would build it “way under budget.” He also said that his plan would include a request for $5 billion for additional security measures along the border.

The fate of the Dreamers is at the center of a furious stalemate in Congress, where Republicans and Democrats are struggling to find a compromise. Mr. Trump’s positions have been difficult to discern, vacillating between his expressions of sympathy for the DACA recipients and his hard-line demands for a crackdown on illegal immigrants.

Mr. Trump campaigned for the presidency with nativist rhetoric that assailed the threat from outsiders, especially Mexicans and Muslims. As president, he quickly tried to impose a travel ban on predominantly Muslim countries and gave immigration agents more authority to round up undocumented immigrants.

But he also once said that he wanted “a bill of love” to address the fate of the DACA recipients.

Senator Tom Cotton, Republican of Arkansas, who is a hard-line conservative on immigration issues, reiterated that any deal on immigration would have to include Republican demands for tougher enforcement on immigration, saying on Twitter that “it must be done responsibly, guaranteeing a secure & lawful border & ending chain migration, to mitigate the negative side effects of codifying DACA.”