The program, initiated under former President Barack Obama in 2012, allows individuals who entered the U.S. prior to their 16th birthday to register to remain in the country, provided they pay a fee and meet certain requirements related to their education and criminal record. Those accepted under the policy -- known as "DREAMers" -- may stay for renewable periods and are eligible for work permits.
Asked Friday if those who are currently protected by the program should be worried, the president responded: "We love the DREAMers. We love everybody."
Earlier in the day, Trump said a decision could be made Friday or this weekend, though he later specified Saturday, Sunday or Monday at the "latest." White House press secretary Sarah Sanders eventually assigned Tuesday as the date for an announcement during Friday afternoon's press briefing.
ABC News reported last week that Trump was leaning toward ending the program.
Trump faces a Sept. 5 deadline when the attorneys general of 10 states plan to file suit against the administration over the policy's continued existence.
Though Trump has maintained an aggressive stance on undocumented immigration from the first days of his presidential candidacy over two years ago, at times he has appeared willing to consider leniency on the DACA policy.
In July, the president said that a decision on DACA would be "very, very hard to make" but that he understood the situation "very well."
A number of lawmakers, including members of Trump's own party, spoke out Friday against the possibility of the president ending the policy, instead arguing for Congress to decide on its future.
"We also need a workable, permanent solution for individuals who entered our country unlawfully as children through no fault of their own and who have built their lives here," read the statement from Hatch. "And that solution must come from Congress."
As of the end of March, almost 788,000 initial grants and 800,000 renewals had been made under the program since 2012.
ABC News' Serena Marshall contributed to this report.