Democrats, wanting a deal for the "Dreamers" - illegal immigrants brought to the U.S. as children who will be at risk of being deported in March - held back on federal funding until Republicans agreed to a discussion on the issue. "Tell them they have nothing to worry about", he said.
"We'll be talking about gun laws as time goes on", Trump said then.
NBC's Peter Alexander grilled White House spokeswoman Sarah Sanders on Wednesday, demanding a presidential statement from Trump letting Americans know "how he feels" about school shootings.
Congress is moving forward with a bipartisan plan to address both border security and undocumented immigrants benefiting from the Deferred Action for Childhood Arrivals program.
The program now protects about 700,000 people, mostly Hispanic young adults, from deportation and provides them work permits.
"This statement represents presidential leadership on immigration that will allow us to solve a hard problem", Graham said in a statement.
Trump also said he is seeking $25 billion for a wall along the border with Mexico, and $5 billion for other security measures.
People protest for immigration reform for DACA recipients and a new Dream Act, in Los Angeles, California, U.S. January 22, 2018.
Around three dozen senators from both parties met privately Wednesday, and two top lawmakers said they'd try crafting a compromise bill based on colleagues' suggestions.
In October a year ago, the Trump outlined his priorities for sweeping immigration reform in exchange for giving legal status to the nearly 700,000 DACA recipients.
Senate Majority Leader Mitch McConnell, R-Ky., has said if senators can not produce a compromise plan by February 8, he would open a debate on immigration legislation that would be "fair to all sides".
Since the partial government shutdown last weekend, Democrats and some Republicans say they are committed to finding a way to shield from deportation the estimated 800,000 young immigrants the program protects.
The White House announcement on immigration came as 35 senators gathered late Wednesday to figure out how the chamber will proceed on its immigration debate.
White House press secretary Sarah Huckabee Sanders talks to reporters during a press briefing in the Brady press briefing room at the White House, Friday, Nov. 17, 2017. "This framework will fulfill the four agreed upon pillars: securing the border and closing legal loopholes, ending extended family chain migration, canceling the visa lottery, and providing a permanent solution on DACA".
"It's gonna happen at some point in the future, over a period of 10-12 years", Trump said.
Yet Trump has reneged on previous statements about the dreamers, who have lived in the country illegally since they were children.