Washington (CNN) The Trump administration's zero-tolerance policy that has resulted in thousands of family separations at the border hasn't deterred immigrants from trying to enter the country illegally, despite the administration's predictions that it would, internal Department of Homeland Security documents obtained by CNN show.

The documents, which refer to the effort as the "Prosecution Initiative," demonstrate that in early April, days after President Donald Trump announced he would send the National Guard to the border and after Attorney General Jeff Sessions announced his offices would prosecute all illegal crossings referred to the Justice Department, Homeland Security staff predicted that the deterrent effects of the policies would be visible quickly.

"The full impact of policy initiatives are not fully realized for 2-3 weeks following public messaging -- however, some migrants already underway may temporarily halt to determine the effects of the new policy," the document states.

Instead, publicly released data showed a roughly 5% uptick in the number of people caught crossing the border illegally when compared to figures from April, including a big jump in unaccompanied children.

While the documents don't speak to the conceptualization of the policy or the internal deliberations that preceded it, they call into question the administration's justification for the policy. The lack of measurable impact on immigration lends weight to questions about the policy's effectiveness, going beyond moral issues raised by the policy's critics.

So far, the policy has resulted in the separations of least 2,000 children from their families.

The administration's decision this spring to begin referring all people caught crossing the border illegally for prosecution -- including those that come with children -- has resulted in those families being separated when the adults are sent to face criminal charges, without clear procedures for reuniting them with their children afterward.

Trump himself has framed the issue by falsely blaming Democrats for family separations, while also suggesting it is mainly a negotiating tactic to force Democrats to accept other hardline measures the administration is seeking.

"Why don't the Democrats give us the votes to fix the world's worst immigration laws? Where is the outcry for the killings and crime being caused by gangs and thugs, including MS-13, coming into our country illegally?" Trump tweeted Monday morning.

Why don't the Democrats give us the votes to fix the world's worst immigration laws? Where is the outcry for the killings and crime being caused by gangs and thugs, including MS-13, coming into our country illegally? — Donald J. Trump (@realDonaldTrump) June 18, 2018

Homeland Security Secretary Kirstjen Nielsen also defended the policy on Monday amid rising criticism. She told "those who have complained" that they should work with the administration to "fix" the laws they take issue with.

"We will not apologize for the job we do or for the job law enforcement does for doing the job that the American people expect us to do," she said, speaking in front of a friendly audience of the National Sheriffs' Association. "Illegal actions have and must have consequences. No more free passes, no more get-out-of-jail-free cards."

JUST WATCHED DHS secretary: We will not apologize Replay More Videos ... MUST WATCH DHS secretary: We will not apologize 00:53

But a month after the administration started generating headlines about family separation, the Homeland Security Department's own data showed the policy did not yet have the desired and predicted effect on the number of people trying to cross the border illegally or the number who show up at a legal crossing without paperwork, but may be claiming asylum.

Government officials repeatedly encouraged would-be border crossers seeking asylum protections to show up at legal ports of entry to claim their protections, touting it as a way to avoid being separated from children.

Meanwhile, in addition to the number of people crossing illegally increasing, the number of people showing up at legal border crossings decreased by 9% that month despite that statistic usually increasing in the month of May, based on historic trends.

While Sessions made the announcement in early April, the issue of family separations did not gain attention until a month later, in May, when the Department of Homeland Security followed suit and said it would refer 100% of the adults it catches crossing the border illegally to the Justice Department for prosecution -- including those coming with children.

"If you're smuggling a child, we're going to prosecute you, and that child will be separated from you probably, as required by law," Sessions said on May 7, when the DHS policy was announced. "If you don't want your child to be separated, then don't bring them across the border illegally."

"Our policy is if you break the law, we will prosecute you," Nielsen testified before Congress a week later. "You have an option to go to a port of entry and not illegally cross into our country."

But weeks later, in a document from late May, staff noted that the policy had not yet had its desired effect, saying it could happen by the end of the month.

"CBP continues to asses that the deterrent effect of the Prosecution Initiative is not yet fully realized and apprehensions may still begin to decline before the end of the month," the document states.

It also said that another predicted outcome of the policy -- that there would be clear statistical evidence that migrants were opting to show up at legal border crossings instead of crossing illegally -- also did not happen, and in fact the opposite seemed to occur.

"There is no evidence of deflection from apprehensions between the ports of entry to the ports (one potential side effect of the Prosecution Initiative)," the document reads.

But the documents and publicly released data showed that nothing changed in the trends before the end of the month: illegal crossings continued to increase each week, and the number of people showing up at legal entries decreased each week.

Experts question if the Trump administration is taking a realistic approach to border security, both in terms of its characterization of the situation at the border currently and what its policies could achieve.

Doris Meissner, a senior fellow and director at the nonpartisan Migration Policy Institute and former high-ranking immigration official across multiple administrations in the Justice Department, said the flows of migrants in North America are affected by a variety of factors pushing them out of their homes and pulling them toward the US.

"Of course these are intended to be deterrent measures," she said of the administration's moves at the border. "The question is, are these kinds of changes in policy, will they really function as a deterrent? And they may, for a while. ... Sometimes there is a pause. But when the underlying conditions continue, the pause will end, just as it did last year after the initial reduced apprehensions that happened once the new administration came into office."

DHS spokeswoman Katie Waldman downplayed the idea the department was expecting sooner results and said the agency "expect(s) the strong message of zero tolerance to take time to reach Central American countries."

"Of course we expect the 100% prosecution policy at the border to have a deterrent effect. The application of consequences for breaking our nation's immigration laws and violating our nation's sovereignty will be effective," Waldman said.

"However, we do not expect those seeking to enter the country illegally to miraculously turn back weeks into their dangerous, illegal journey just because they have heard of a new enforcement policy," she added.

Meissner said the administration should take a "longer view" of the issue and realize that addressing migration requires multi-layered policy that both has a fair but efficient system for handling claims in the US and a policy that seeks to improve conditions in the Central American countries they are fleeing -- countries Meissner points out are US allies and developing democracies. She said it took months to address the child migrant crisis of 2014, when numbers of crossings far outpaced what the US is currently seeing, and that the key wasn't messaging, but rather recruiting the Mexican government to turn back migrants within its borders -- something it continues to do at paces exceeding the US.

"There have to be changes in each dimension of what makes up the issue," Meissner said. But, she added, "We really are in unknown territory on this, because these sorts of measures are well beyond what we ever tolerated as a country or thought to do as a country."