WASHINGTON — 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Twitter contrasted with efforts by congressional allies to respond to the highly unpopular administration policy, now rescinded, of automatically taking minors away from parents apprehended at the border.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 an additional roughly 10,000 children who had arrived at the border without their 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 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.”

With the controversy over the separations only partly abated, 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.

At a recent, contentious White House news briefing, Press Secretary Sarah Huckabee Sanders erroneously said the policy was mandated by law, adding that its enforcement was “biblical.”

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.

Lankford, who has moved to spearhead a short-term congressional fix on the family separation issue, acknowledged that Trump’s rhetoric on immigration has been polarizing.

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.

Trump partisans have traded heavily on this notion, and the president has signaled determination to make the purported security threat posed by immigrants a central issue in this year’s midterm elections.

“Our issue is strong borders, no crime,” Trump told the crowd in Nevada. Referring to Democrats, he said: “Their issue is open borders.”

“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.”

Trump has repeatedly blamed Democrats for his administration’s family separation policy, and on Sunday he again asserted that the Democrats, despite having control of neither house of Congress, were responsible for the lack of a legislative solution. “Don’t RESIST,” he wrote in a Twitter post.

Sen. Bernie Sanders (I-Vt.), appearing on CNN’s “State of the Union,” said Trump’s own self-contradicting actions and statements had hampered prospects for a bipartisan measure.

“Clearly, anyone who looks at the record understands that the Democrats have been serious about comprehensive immigration reform,” Sanders said. “We have a president who’s not serious about policy,” he added.

Sen. Angus King of Maine, also an independent, said the administration was neglecting the fact that most of the people illegally crossing the border in recent years were fleeing violence in Central America.

“That’s one of the reasons this idea of a deterrent may not work,” King said on “Meet the Press.”

“If you’re looking down the barrel of a gun in your home community, whatever your chances are to get to a free country, you’re going to take it in order to save your family’s lives,” he said. “So that really is what we’re talking about here.

“And this is very different from the waves of illegal immigrants coming across the border 15, 20 years ago, mostly from Mexico, simply looking for jobs. Mexican migration has diminished enormously.”

Interviewed on CNN, Rep. Barbara Lee (D-Oakland) called for urgent action to reunite children taken from their parents and demanded an investigation of the administration’s actions.

“These children are traumatized.… They have no ability to defend themselves,” Lee said after a visit to two child-migrant shelters in Texas. “This is child abuse, and child abuse is a violation of human rights.”

Even some Republicans were reluctant to put their personal credibility on the line in predicting timely reunions of migrant children with their parents. Asked on “State of the Union” whether the government knew which kids belonged to whom, Sen. Ron Johnson (R-Wis.) replied: “That is what they are claiming.”

Pressed as to whether the federal government has the ability to bring about the promised reunions, Johnson, who chairs the Senate Homeland Security Committee, replied: “They are saying they do.”

laura.king@latimes.com

Twitter: @laurakingLAT