A senior White House official told CBS News Friday that the Trump administration had "floated" a proposal to release immigrant detainees into so-called "sanctuary cities," but claimed the idea was rejected. President Trump, however, said Friday that he is still considering the idea.

The Washington Post first reported that officials had proposed transporting migrants to sanctuary cities at least twice in the last six months alone -- both taking place at a time when the administration was pressed on its immigration standpoints. The White House official told CBS News on Friday, "This was just a suggestion that was floated and rejected, which ended any further discussion."

But later Friday afternoon, Mr. Trump tweeted that the administration would be giving "strong considerations to placing Illegal Immigrants in Sanctuary Cities", blaming congressional Democrats for not tightening immigration laws.

Due to the fact that Democrats are unwilling to change our very dangerous immigration laws, we are indeed, as reported, giving strong considerations to placing Illegal Immigrants in Sanctuary Cities only.... — Donald J. Trump (@realDonaldTrump) April 12, 2019

The president's tweet comes as his administration is looking to implement even more aggressive immigration policies after replacing top leaders at the Department of Homeland Security, including former DHS Secretary Kirstjen Nielsen.

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Asked about the idea to place illegal immigrants in sanctuary cities during an event on 5G at the White House, the president reiterated he's looking at that.

"We are looking at he possibility, strongly looking at it to be honest with you," Mr. Trump said, adding later the federal government could give California an "unlimited supply" of immigrants in the country illegally.

"If they don't agree we night as well do what they say they want ... we'll bring them to sanctuary city areas and let that particular area take care of it," the president also said.

Asked about the seeming discrepancy between the two statements, White House Principal Deputy Press Secretary Hogan Gidley said, "Democrats say we must have open borders and that illegal immigrants have a right to be in this country at all costs, so they should be working with the administration to find the best ways to transport those illegal aliens that are already set for release, into communities in their districts and states."

The Post reported that the proposal was intended to act as payback against President Trump's political foes in areas where undocumented immigrants, who might otherwise be deported, could be offered a safe harbor. There are currently over 140 sanctuary jurisdictions -- cities and counties -- across the U.S., including at least 37 cities -- San Francisco, New York, Chicago, Seattle, Miami and Los Angeles, among others.

Another administration official called the suggestion a "non-story." The proposed idea would help process the heavy influx of illegal immigration by releasing some to sanctuary cities because they were already open to taking them -- not because of political reasons, according to the officials who spoke on background.

The Trump administration has actively tried to crack down on sanctuary cities across the country over the past few years. The president has condemned leaders in these cities as skirting immigration laws in order to harbor "dangerous criminals."

In 2017, Mr. Trump signed an executive order that would withhold federal grant money from sanctuary cities. That order was later deemed unconstitutional by a U.S. appeals court. The administration later sued the state of California for what the Department of Justice viewed as interfering with federal immigration laws by acting as a sanctuary city.

The administration is now looking to change a handful of key immigration-related policies, even as the president continues his threats to shut down the border. Specifically, the White House intends to change rules to allow the government to detain migrant families for longer than the current 20-day limit imposed by what's known as the Flores agreement, according to a senior administration official.

The White House also wants to make it more difficult for immigrants to be approved for asylum, the official said, claiming approval rates are too high.

San Francisco District Attorney George Gascón responded to the president's proposal by claiming sanctuary jurisdictions like San Francisco have less crime.

"With immigrants being less likely to commit crimes than the U.S. born population, and with sanctuary jurisdictions being safer and more productive than non-sanctuary jurisdictions, the data damns this proposal as a politically motivated stunt that seeks to play politics with peoples' lives," Gascón said in a statement. "The fact that such a proposal is being peddled by the leader of the free world is an all-time low for American discourse, and it's the clearest sign yet that the president fully intends to chart a path to reelection on the back of racist rhetoric and policies intended to divide us."

Emily Tillett, Kathryn Watson, Katiana Krawchenko and Fin Gomez contributed to this report.