Fox News host Shepard Smith on Tuesday fact-checked President Trump after Trump claimed former President Obama separated children from their families at the U.S.-Mexico border.

Smith said on his show that he was "separating rhetoric from reality when it comes to immigration in America" before outlining the history of family separations at the border.

During a scrum with reporters at the White House on Tuesday, Trump claimed that "Obama separated the children, by the way."

"Those cages that were shown - I think they were very inappropriate. They were built by President Obama's administration, not by Trump," Trump said. "President Obama had child separation."

Trump previously criticized pictures from 2014, under the Obama administration, of unaccompanied migrant children detained at the border that were widely shared on social media shortly after the Trump administration began separating children from their parents.

Trump's previous policy separated children from their families even if they crossed the border together.

Smith pointed out inaccuracies in Trump's comments, saying, "President Trump has made similar claims before. Following are the facts."

Smith said while former presidents had policies to apprehend and deport migrants who were in the country illegally, officials from the George W. Bush and Obama administrations "gave children a pass."

He said while there were exceptions under the Obama administration, "it was not the policy to separate."

"After President Trump issued the zero tolerance order, officials did separate children from their parents," Smith said. "Some families have not yet been reunited."

He added that "the Trump administration did separate families. The Trump Department of Homeland Security estimates more than 2,300 children had been separated from their families by last spring. The Trump administration did detain children in cages."

Trump said Tuesday he will not reinstate a plan to separate children from their families at the border.

Smith's fact check echoed that of CNN anchor John King, who said Tuesday afternoon his network is "going to need a backup generator for the fact check machine" following President Trump's comments regarding family separation policy and blaming Democrats for the current impasse on a comprehensive immigration solutions.

"We're going to need a backup generator for the fact check machine for part of what the president said there, including his bit about blaming the Democrats," King said to his panel on "Inside Politics."

"The Democrats now control the House. The Democrats disagree with a lot of what he wants in immigration policy, but this president walked away from a deal when the Republicans controlled the Congress that would have given him a lot more funding for his border wall than he has now, would have given some of the enforcement mechanisms that he wants now and could never get through a Democratic-controlled house," the anchor continued.

"So when he keeps blaming the Democrats - they have policy disagreements - but he walked away from a deal because he didn't want to give the 'Dreamers' status that was just about done."

"That was one thing there. Yes, President Obama did have some family separation policies, and, yes, some of those early images were from the Obama administration. But the Trump administration accelerated the family separation policy. [Trump] said, 'I stopped it.'"

Joe Concha contributed to this report.