Sen. Marco Rubio (R-Fla.) is an immigration reform advocate. (AP File Photo)

(CNSNews.com) - President-elect Donald Trump campaigned on a promise to rescind many of President Obama's executive orders, and some illegal aliens fear the DACA program -- Deferred Action for Childhood Arrivals -- may be one of the executive actions to die at the stroke of Trump's pen.

Sen. Marco Rubio (R-Fla.), an immigration reform advocate, told NBC's "Meet the Press" on Sunday he would recommend that Trump leave the DREAMers' temporary legal status in place, but not renew it when the two-year deferral period is up.

"I would not retroactively remove their status," Rubio said of the DREAMers. "I would say that, from some point forward, people will not be allowed to apply for renewal for that status. And that will give us (Congress) a defined period of time to work through this, beginning with border security and modernization of the legal immigration system."

Since the DACA program took effect in 2012, hundreds of thousands of people who were brought to the United States illegally as children have signed up for a two-year reprieve from deportation along with work permits.

But Rubio noted that the reprieve is not indefinite: "It expires," he said.

"And what I would say is, if you have it, you will have it for the remainder of that period of time. But you will not be able to renew it.

"In the meantime -- and it's not a long period of time. But it does give us the time to do border security, modernization and then move to something very reasonable for people like those who came here as children or those who have been here for a long time, who are not criminals, to allow them to attain some legal status through a legal way, not an unconstitutional way, which is what DACA is."

Rubio in 2013 was among the sponsors of an immigration overhaul bill that included a pathway to citizenship for millions of illegal aliens. The bill died in the House of Representatives.

During the presidential primary this past February, Rubio told CNN's Jake Tapper that DACA "has to go away, and it will."

"I will, on my first day in office, get rid of it because it's unconstitutional," Rubio added.

During the primary season, Donald Trump called for a deportation force to send illegal aliens out of the country, but he later backed off on that, saying he would focus his deportation efforts on the most dangerous criminal illegal aliens.

In a major address on immigration this past August, Trump addressed illegal aliens who want to remain in the United States:

"For those here today illegally who are seeking legal status, they will have one route and only one route: to return home and apply for re-entry under the rules of the new legal immigration system that I have outlined above. Those who have left to seek entry under this new system will not be awarded surplus visas, but will have to enter under the immigration caps or limits that will be established.

"We will break the cycle of amnesty and illegal immigration. There will be no amnesty. Our message to the world will be this: you cannot obtain legal status, or become a citizen of the United States, by illegally entering our country."