Nearly 2,000 children from Central America and elsewhere are now being held by U.S. authorities after being separated from their parents along the Southwest border, the Department of Homeland Security said Friday.

That word came as DHS and Justice Department officials held a conference call to admonish the news media for what they described as misguided reporting about the family separation issue that they claimed has been based on "anecdotal, exaggerated and often fictional accusations."

With the Trump administration vowing "zero tolerance" for illegal immigration and warning that it intends to prosecute one hundred percent of those who illegally cross the U.S.-Mexico border, children whose parents are referred for prosecution by the Justice Department are left behind in the custody of the Border Patrol, Health and Human Services or other U.S. agencies.

On Thursday, HHS confirmed that the Tornillo Land Port of Entry in Texas will be used to house an overflow of hundreds of unaccompanied children. HHS says the facility is comprised of “soft-sided structures with air conditioning," and it could house both unaccompanied minors that cross the border alone and children separated from their parents.

A DHS official said Friday that from April 19 through May 31, a total of 1,995 minors traveling across the U.S. border with "alleged adult guardians" were transferred to the custody of the Border Patrol.

"Fundamentally with the one hundred percent prosecution policy, we are left with the choice of whether to enforce the law at the border or to allow individuals who enter the country with children ... to go free and not face consequences for their illegal action," the official said, speaking to reporters on the condition of anonymity. "Advocates ... want illegal aliens to get better rights than U.S. citizens have. Every day in America, if you commit a crime, you will be separated from your family as you are prosecuted and face the consequences of that criminal conduct."

One DHS official on the conference call said authorities have seen emotion "overtake the facts," and, "We would like to correct the record." The DHS official, however, refused multiple requests for him to speak on the record, with his name used, about his concerns.

The DHS official said that – even in the midst of its "zero tolerance policy" – DHS would never separate breastfeeding children from their parents. The official also said that despite reports to the contrary, DHS works "as much as possible" to help separated children stay in touch with their parents.

But, the official acknowledged, those children's parents "are in jail settings" and communication "may be limited," as would be the case in any criminal proceeding across the country. The official said DHS has established a telephone hotline and "other ways" for parents to keep tabs on their children.

The DHS official also complained about media reports suggesting U.S. officials are turning away asylum seekers at the border and not allowing those travelers to make their claims.

"That's not true at all, that has not happened," the DHS official insisted. "Anyone who enters the country and makes a claim for asylum will see their day in court, they will have their claim heard."

And finally, the DHS official disputed what he called "absurd claims" from a member of Congress who said there is no clean drinking water at federal facilities.

Earlier this week, Rep. Pramila Jayapal, a Washington state Democrat, visited a federal detention facility near Seattle that is holding nearly 200 mothers referred for prosecution. Days later, Jayapal posted a series of messages to Twitter about the women she met.

"They are fleeing rape, violence and persecution," Jayapal wrote. "Many of them are asylum seekers, but Trump's deportation force is treating them like they aren’t even people. ... They spent time in frigid facilities—a place they call the 'ice box.' They were held in kennel-like cages—a place they called the 'dog pound.' For days on end, they wouldn't have clean water to drink. They don't know where their kids are. They didn't even get to say goodbye. ... Family separation is not who we are as a nation. We will not stand for it."

Speaking to reporters on Friday, the DHS official said such claims of no clean drinking water are "just completely false." The official did not specifically address other claims made by the member of Congress.

--ABC News' Geneva Sands contributed to this report.