Democrats responded skeptically Sunday to the Trump administration’s assertion that it has a process in place to reunite more than 2,000 “separated minors” with their parents, while Republican lawmakers sought to defend the president’s immigration policies and again promised that all the children taken from their parents in recent weeks were accounted for.

Trump himself, however, redoubled his denunciation of all unauthorized arrivals, even those engaging in the legal act of seeking asylum. In a message on Twitter, he suggested that people crossing the border should be deported summarily, without a court hearing.

“We cannot allow all of these people to invade our Country,” he wrote. “When somebody comes in, we must immediately, with no Judges or Court Cases, bring them back from where they came.”

Despite Trump’s language about invasion, the flow of people crossing the border illegally remains low compared with just a few years ago, although numbers are higher than they were last spring, in the months just after Trump took office.

The president’s hard line on Twitter contrasted with efforts by congressional allies to respond to the highly unpopular administration policy, now rescinded, of automatically taking minors away from parents apprehended at the border.

Even a prominent GOP ally of Trump’s acknowledged frustration over the lack of information from the White House after the enormous nationwide furor over the family separations.

“I don’t, actually,” Sen. James Lankford of Oklahoma responded when asked on NBC’s “Meet the Press” whether he thought the White House had been fully transparent about its handling of the issue. In the same interview, however, Lankford insisted that “we know where every single child is.”

Immigration advocates and Democratic lawmakers have voiced alarm and outrage over the fact that Trump’s executive order last week reversing himself on the policy of separating families did not incorporate any pledge to swiftly reunite them.

Late Saturday, the Department of Homeland Security and the Department of Health and Human Services said in a joint statement that the government still had 2,053 “separated minors” in its custody and another roughly 10,000 children who had arrived at the border without parents.

The statement said a formal process had been established to return the separated minors to their parents, centered at the Port Isabel detention center near the Texas Gulf Coast north of Brownsville.

The statement said that 522 migrant children had been reunited with their parents, although it did not say how many, if any, of those had been reunited since Trump signed his order on Wednesday.

“The United States government knows the location of all children in its custody,” the statement read, but it did not claim that the government knows who or where all the children’s parents are. The government “is working to reunite them with their families,” the statement said. “This process is well coordinated.”

No senior administration official went on the Sunday news-talk shows to defend the White House’s actions, as would be normal practice when a major policy issue is involved.

There also has also been no White House press briefing since a contentious session on Monday, when spokeswoman Sarah Huckabee Sanders erroneously said the policy was mandated by law.

Sanders became embroiled in controversy over the weekend after she was asked to leave a restaurant in Lexington, Va., and subsequently used her government Twitter account to identify the establishment involved. That raised questions of the ethics of shunning people over political differences as well as whether Sanders had violated government ethics rules by using an official platform to single out a private business.

In a speech Saturday in Las Vegas, Trump blamed a “tremendous” surge in violence on immigrants, despite the fact that violent crime in the U.S. has declined in recent years, not surged, and studies that show immigrants, both legal and illegal, do not commit crimes at higher rates than non-immigrants.

“Meet the Press” host Chuck Todd asked Lankford whether language used by Trump — who has referred to immigrants as “animals” and likened mass arrivals to an infestation — “makes your job harder” by demonizing immigrants.

Lankford replied: “It does, actually.” He added, though, that “there is a percentage where the president is absolutely correct on that.”

laura.king@latimes.com