By Daniella Diaz and Eli Watkins, CNN

(CNN) -- Oregon Sen. Jeff Merkley returned to the South Texas border on Sunday with a group of Democratic colleagues to tour the Customs and Border Protection processing centers in the Rio Grande Valley.

The lawmakers came to South Texas, they say, to learn more about the agency's processing of undocumented immigrants entering the United States, including a policy to refer all people who cross the border illegally for criminal prosecution on top of immigration proceedings.

As a result of enforcing that policy, families who cross illegally have been separated from their children because those accompanying the children are put into the criminal justice system.

The group included Sen. Chris Van Hollen of Maryland, Texas Reps. Filemon Vela, Vicente Gonzalez, and Sheila Jackson Lee, Vermont Rep. Peter Welch, Rhode Island Rep. David Cicilline, and Wisconsin Rep. Mark Pocan.

Both Gonzalez and Vela represent parts of the Rio Grande Valley in Congress.

Speaking after visiting a processing center in McAllen, Texas, several Democrats expressed anger at the family separations and called on the Trump administration to change its policy.

"When you have a mother tell you directly that she's in fear that she will never see her child again, and when the United Nations Human Rights Commission indicate to the Trump administration that you are violating human rights, then you know that what we are saying today is President Trump, cease and desist," Jackson Lee said.

Merkley said he had "spoken directly" with Attorney General Jeff Sessions about the policy and wanted to see if President Donald Trump would meet with them.

"We must end this policy of family separation," Merkley said.

Treatment of asylum seekers

Merkely also addressed the issue of those legally seeking asylum being separated from their families at the border. He told CNN's Ana Cabrera that he had heard "a number of stories of people who did cross at the official checkpoints who have also been charged with a crime and separated from their children."

Republican Sens. Susan Collins of Maine and Jeff Flake of Arizona, raised the issue in a Saturday letter to the departments of Homeland Security and Health and Human Services. The letter cites reports about a Honduran mother who sought asylum by presenting herself to authorities at an international bridge in Brownsville, Texas, and was separated from her 18-month-old child for months, as well as a similar case in Southern California.

The senators requested that the departments explain how and why family separations are occurring, if there are procedures in place to keep parents informed about their children and if the personnel who handle the children have training to make "the separation process less traumatic."

Later Sunday, Homeland Security Secretary Kirstjen Nielsen posted a statement on Twitter focusing on asylum seekers and denying any policy of separating families at the border.

"This misreporting by Members, press & advocacy groups must stop. It is irresponsible and unproductive," Nielsen wrote. "As I have said many times before, if you are seeking asylum for your family, there is no reason to break the law and illegally cross between ports of entry."

"You are not breaking the law by seeking asylum at a port of entry," she continued.

"For those seeking asylum at ports of entry, we have continued the policy from previous Administrations and will only separate if the child is in danger, there is no custodial relationship between 'family' members, or if the adult has broken a law," Nielsen added.

A Homeland Security official told CNN that the secretary "is in lockstep with the President on this," but added she is "frustrated" over news coverage that the administration believes to be inaccurate. The source added that department officials are vigorously working to investigate the veracity of the reports because they believe "most of those stories are not all the way true."

Asked about Nielsen's tweet that the administration does not have family separation policy, the official said the department is simply doing more than previous administrations to enforce legislation already on the books.

"It is not a policy, but it is a byproduct of what we're doing," the official said.

'Next Steps for Families' Customs and Border Protection provided CNN with a document titled "Next Steps for Families" during a walk-through of a processing center in McAllen. The document lists several steps for those in the government's custody and includes several actions for people to take under the question "how do I locate my children," including telephoning agency call centers and hotlines or emailing them.

CNN's Dianne Gallagher reported after a tour of the processing center that families are brought through the warehouse and separated by the adults' gender, and that one woman approached CNN, crying and expressing fear about what would happen next.

The visit comes two days after the Department of Homeland Security confirmed the US government has separated nearly 2,000 children from parents at the border since implementing a policy that results in such family separations.

From April 19 through May 31 of this year, 1,995 minors traveling with 1,940 adults who said they were the children's guardians were separated due to the policy, Department of Homeland Security spokesman Jonathan Hoffman told reporters Friday on a conference call.

Merkley first visited the South Texas border on June 3, where he was denied entry to an immigration center for unaccompanied minors in the border city of Brownsville after asking for a tour of the facility.

"It's damaging to children, putting them through a horrific experience in a land where they know no one and they don't know where they're being sent and don't understand why they're being sent just as a way to be, if you will, cruel as a strategy of deterrence -- not deterrence from people crossing the border, deterrence from people seeking asylum," he said at the time.

White House press secretary Sarah Sanders argued Thursday that it's "biblical" for the Trump administration to enforce federal law in a way that separates children from their families at the border when they illegally enter the US. Her comments came when she was pressed by CNN's Jim Acosta on whether she agreed with Attorney General Jeff Sessions' assertion, citing Romans 13, that the Bible requires the Trump administration to follow the law.

The Catholic Church and other religious leaders have voiced strong criticism of policies resulting in family separations and recent moves Sessions has made to restrict asylum. Cardinal Timothy Dolan, a prominent Catholic leader in the United States, said Friday there is no biblical defense for separating families, condemning the practice as "unjust" and "un-American."

Human rights organizations also argue it's inhumane to separate children from their parents.

The American Civil Liberties Union has a petition on its website to request the Department of Homeland Security stop separating immigrant children from their parents.

"The Trump administration is sending the clear message that immigrants aren't welcome here -- and they don't mind sacrificing constitutional rights and basic human decency just to get that across," the petition states. "They want to scare people away from coming to this country to seek a better life and aren't afraid to admit it."

In Congress, Senate Judiciary committee ranking member Dianne Feinstein introduced the Keep Families Together Act, a bill that would prevent the separation of immigrant children from their parents.

Democratic Rep. Jerry Nadler, ranking member on the House Judiciary Committee, is planning to introduce the companion bill on the House side, a source told CNN.