On the DACA negotiations, the President also said he wants other immigration enforcement measures, like an end to chain migration, and the end of a visa lottery program.
In his news conference with reporters, the President also faced a series of questions about a new book from author Michael Wolff, as Mr. Trump made clear he felt the book was totally off base, labeling Wolff "a fraud," and calling the book a "work of fiction."
"I never interviewed with him at the White House," the President declared.
In several exchanges with reporters, the President also took aim at former top aide Steve Bannon, whose quotes in the Wolff book angered Trump and other White House officials.
"I don't know this man, I guess Sloppy Steve brought him into the White House quite a bit," the President said, using his new nickname for Bannon. "That's why Sloppy Steve is now looking for a job."
Mr. Trump was also pressed by reporters on stories in recent days that said his White House counsel had asked Attorney General Jeff Sessions not to recuse himself from the investigation into Russia's interference in the 2016 elections.
The President said a New York Times story on the subject was wrong, but refused to say what was in error - only that his own actions, and those of his White House were all above board.
"Everything you read about that is 100 percent proper," the President said, sidestepping more direct questions about the matter, as he declared again that there was no collusion between his campaign and Russia in 2016.
As for this year's GOP legislative agenda in the Congress, notably absent was a mention of welfare reform, which President Trump had talked about in recent weeks.
Asked about that, Mr. Trump seemed to indicate that would be something addressed only with Democrats on board.
"We'll try and do something in a bipartisan way, otherwise we'll be holding it for a little bit later. But we'll be looking to do that very much in a bipartisan way, if we can," the President added.