The number of migrant children held in U.S. government custody without their parents has surged 21 percent in the past month, according to the latest figures, an increase driven by the Trump administration's "zero tolerance" crackdown on families who cross the border illegally.

Although the government has not disclosed how many children have been separated from their parents as a result of the new measures, the Department of Health and Human Services said Tuesday, May 29, that it had 10,773 migrant children in its custody, up from 8,886 on April 29.

Under the "zero tolerance" approach rolled out last month by Attorney General Jeff Sessions and Homeland Security Secretary Kirstjen Nielsen, anyone who crosses into the United States illegally will face criminal prosecution. In most cases, that means parents who arrive with children stay in federal jails while their children are sent to HHS shelters.

Those shelters are at 95 percent capacity, an HHS official said Tuesday and the agency is preparing to add potentially thousands of new bed spaces in the coming weeks. HHS also is exploring the possibility of housing children on military bases but views the measure as a "last option," according to the HHS official, who spoke on the condition of anonymity to discuss the agency's preparations.

HHS has about 1,300 reserve beds to accommodate more children, the official said, including several hundred at a government-owned building in Homestead, Florida, adjacent to an Air Force base previously used as a Labor Department training center.

In a statement, Kenneth Wolfe, a spokesman for HHS' Administration for Children and Families, said that the agency has "an existing network of approximately 100 shelters in 14 states" and that "additional temporary housing is only sought as a last resort when current locations are reaching capacity."

The latest figures do not distinguish between minors who arrive without a parent and those who are separated from their mothers and fathers after they cross the border. But an official for U.S. Customs and Border Protection testified at a Senate committee hearing last week that 638 adults were referred for prosecution between May 6 and May 19 under the new zero-tolerance effort and that they brought 658 children with them.

As the scope of the family-separation measures becomes clearer, President Donald Trump's immigration advisers pushed back Tuesday at false or misleading stories about their policies that circulated widely on social media over the weekend. Many seized on reports that HHS "lost" 1,475 children last year, describing them as "missing."

But those reports were based on misleading characterizations of a follow-up phone survey conducted by HHS when it attempted to reach the adult sponsors of migrant children 30 days after releasing them to the sponsors.

HHS does not have a formal responsibility to track children once they are released to sponsors. Agency officials say that is the immigration court system's job. And because many adult sponsors, including parents, are living in the country illegally, they may fear contact with federal officials.

"In the last fiscal year, in 14 percent of those calls, the family didn't answer the phone," a top HHS official, Steven Wagner, told reporters Tuesday. "But there's no reason to believe that anything has happened to the kids. If you call a friend and they don't answer the phone, you don't assume that they've been kidnapped."

Trump officials also gave new details Tuesday about an agreement between HHS and the Department of Homeland Security that immigrant advocates warn could further increase the number of children in federal custody and how long they stay there.

The agreement will give Homeland Security more access to the personal information of parents, relatives or other adult sponsors seeking custody of the children.

In the past, that information was largely walled off for the purposes of immigration enforcement while the sponsors were vetted by HHS, out of a concern that Homeland Security's involvement could have a "chilling effect" on parents living in the country illegally and discourage them from claiming the kids.

But under Trump, senior officials at U.S. Immigration and Customs Enforcement have recommended such measures to deter parents from attempting to send for their children while knowing they can get custody with little fear of deportation.

Wendy Young, president of the advocacy group Kids in Need of Defense, said Homeland Security is "injecting a law enforcement approach into this system," one that will strain HHS bed space.

Homeland Security officials declined to say Tuesday whether the information will be used to target parents for arrest and deportation, characterizing the new measures as an effort to protect children.

"If somebody is unwilling to claim their child from custody because they're concerned about their own immigration status, I think that de facto calls into question whether they're an adequate sponsor and whether we should be releasing a child to that person," Wagner said.

"Plus, we have the problem of people fraudulently claiming to be parents when, in fact, they're not," he added, saying the agreement would give the agency better tools to check sponsors' backgrounds and verify their identities.

In recent months, the average time children spent at HHS shelters increased from 51 to 56 days, according to the agency's latest statistics. Last year, HHS took custody of more than 40,000 migrant children, and the agency's Office of Refugee Resettlement said it released 93 percent to adult sponsors. In half of those cases, the adult sponsor was one of the child's parents, and another 40 percent were close adult relatives.

Jonathan Rath Hoffman, chief spokesman for the Department of Homeland Security, described the Trump administration's determination to prosecute parents as a continuation of Obama-era measures.

"This policy has not changed from the prior administration," he said.

In 2016, more than 20 percent of those who crossed the border illegally faced criminal charges, according to Homeland Security data. During President Barack Obama's second term, the government prosecuted roughly 70,000 cases per year.

Trump critics say that claim is specious and obfuscates the current administration's break with standard practice.

"What's happened is the exception to the rule is now becoming the rule," said Young, who said prosecutions under Obama were far more selective. "Here they're doing zero-tolerance policy to punish families and send a message to their home countries: Don't do this."

"It's so disingenuous to couch this as a continuation" of Obama's policies, Young said. "This is the most aggressive response to Central American migration we've seen to date."

Trump has lashed out at Nielsen and other aides because the number of people illegally crossing the Mexican border has spiked, robbing his ability to campaign on promises of improved border security.

White House Chief of Staff John Kelly first floated the idea of separating families last year, calling it a tool to discourage migrants from attempting the journey. More recently, he caused an uproar when he appeared to dismiss experts' warnings that separating children from their parents inflicts emotional and psychological damage to the kids, saying they'll "be taken care of - put into foster care or whatever."

In a tweet Saturday, Trump portrayed the family-separation measures as a tactic to arm-twist his opponents.

"Put pressure on the Democrats to end the horrible law that separates children from there [sic] parents once they cross the Border into the U.S.," he wrote.

"Trump called the practice 'horrible,' so if he thinks it's so horrible he ought to end it and not make children pawns as a negotiating tool," said Lee Gelernt, an immigration attorney with the American Civil Liberties Union, which has filed a class-action lawsuit to force the government to stop separating families at the border.

"Little kids are begging and screaming not to be taken from parents, and they're hauled off," Gelernt said. "Parents are telling their older kids, 'Be brave, be brave.'

"It's as bad as anything I've seen in 25-plus years of doing this work," he said.

Story by Nick Miroff. Miroff covers drug trafficking, border security and transnational crime on The Washington Post’s National Security desk. He was a Post foreign correspondent in Latin America from 2010 to 2017, and has been a staff writer since 2006.