In attempting to end it in September, Trump argued that Obama's actions were unconstitutional and an overreach of executive power.
Trump's tweets came just hours after his administration resumed receiving renewal applications for "Dreamers" under the Deferred Action for Childhood Arrivals program following a federal court order blocking the administration from ending the program.
He also said he wants a DACA deal to include a merit-based system of immigration and "people who will help take our country to the next level".
Then-President Barack Obama created DACA by executive order in 2012, but Trump announced past year that he was discontinuing it and gave lawmakers until March 5 (when the program is set to expire) to come up with a permanent legislative solution for these young migrants, who otherwise could face deportation even though for many of them the United States is the only country they have ever called home.
The Trump administration had begun phasing out the program in September and meant to terminate it on March 5.
Republican Sens. Tom Cotton of Arkansas and David Perdue of Georgia, who were also in the meeting and have been close allies to the President on the issue of immigration, said in a statement that they didn't recall Trump making the derogatory comments, "but what he did call out was the imbalance in our current immigration system, which does not protect American workers and our national interest".
President Donald Trump had criticized the judicial process, noting that the ruling could still be overturned.
Trump has said any DACA deal would require funding for his proposed border wall along the U.S. -Mexico border.
The proposal included a pathway to citizenship for undocumented immigrants who came to the USA as children and $1.6 billion toward a border fence, two sources with direct knowledge told CNN. This is the time but, day by day, they are blowing the one great opportunity they have.
But that agreement was cast into doubt the same day when a firestorm erupted after reports surfaced that President Donald Trump, during a meeting with lawmakers over an immigration bill, asked why the US was accepting immigrants from "s-thole countries" referring reportedly to immigrants from Africa.
One of the Democratic senators at the meeting, Dick Durbin of IL, confirmed on Twitter that Trump used the term "shithole". "They are all talk and no action", Trump tweeted.