Secretary of Homeland Security Kirstjen Nielsen speaks at the National Sheriffs' Association convention in New Orleans, Monday, June 18, 2018.

Amid the widespread outcry over the Trump administration's policy of separating children from families that illegally cross into the U.S., Attorney General Jeff Sessions and Homeland Security Secretary Kirstjen Nielsen are not backing down.

The two Cabinet members defended the policy, which has seen nearly 2,000 children separated from their families since Sessions issued his "zero tolerance" directive in April, in speeches to the National Sheriffs' Association Monday morning.

"We do not want to separate children from their parents. We do not want adults to bring children into this country unlawfully, placing them at risk," Sessions said, according to prepared remarks.

But, he added, "We cannot and will not encourage people to bring their children by giving them blanket immunity from our laws."

Nielsen, who spoke before Sessions, told the crowd, "We have to do our job. We will not apologize for doing our job. We have sworn to do this job."

Sessions authored an April 6 memorandum directing U.S. attorneys "to adopt a policy to prosecute all" such violations "to the extent practicable." In the six weeks following that order, 1,995 children had been separated from their parents, a Department of Homeland Security spokesman told news outlets on Friday.

Nielsen had tweeted over the weekend that her department does "not have a policy of separating families at the border. Period." The statement appeared to contradict not only the policy itself, but other Trump administration officials who had discussed it.

White House immigration policy advisory Stephen Miller, for example, recently told The New York Times: "It was a simple decision by the administration to have a zero tolerance policy for illegal entry, period. The message is that no one is exempt from immigration law."

And in remarks on Thursday, Sessions explained that "our policies that can result in short-term separation of families is not unusual or unjustified."

At the National Sheriffs' Association event on Monday, Nielsen touted the administration's hard-line approach to prosecute all immigrants who illegally enter the U.S.

"This administration has a simple message: If you cross the border illegally, we will prosecute you. If you make a false immigration claim, we will prosecute you. If you smuggle illegal aliens across an extraordinarily dangerous journey, we will prosecute you," she said.

President Donald Trump echoed that pugnacious tone in remarks at the White House later on Monday. After again blaming Democrats for the policy itself, Trump vowed that "the United States will not be a migrant camp ... not on my watch."

In her remarks, however, Nielsen encouraged immigrants to seek asylum through the proper channels. "If you are seeking asylum, go to a port of entry," she said.