WASHINGTON (Reuters) - A top U.S. official said on Sunday the U.S. border is not open to illegal entry into the country, but acknowledged the government does need to be sensitive to the tens of thousands of migrant children flowing into detention centers.

More than 52,000 unaccompanied minors from Guatemala, El Salvador and Honduras have been caught trying to sneak over the U.S.-Mexico border since October, double the number from the same period the year before. Thousands more have been apprehended with parents or other adults.

"We have to do right by the children, but at the end of the day, our border is not open to illegal migration and we will stem the tide," Jeh Johnson, the U.S. Secretary of Homeland Security, said on NBC's "Meet the Press" on Sunday.

Johnson said that the government administers deportation proceedings to illegal migrants seized at the border, including children. But he added that the government is looking at being more flexible toward the children seized at the border.

"We are looking at ways to create additional options for dealing with the children, in particular, consistent with our laws and our values," Johnson said.

Johnson repeated the stance, taken by President Barack Obama last week, that the president would take executive action to revamp the U.S. immigration system.

"There are a number of things the president and I, within the confines of existing law, can do to fix the broken immigration system. If Congress doesn't act, we will," Johnson said.

Johnson would not answer a question on the Sunday show pertaining to whether the U.S. government would deport the current wave of Central American children, saying only that U.S. authorities would stem the tide, and that deportation processes are commenced against illegal immigrants.

U.S. immigration officials say the crisis is being driven by a mix of extreme poverty, gangs and drug violence in Central America, as well as rumors perpetuated by human smugglers that children who reach the U.S. border will be allowed to stay.

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Critics say that the Obama administration has not moved quickly enough to address the problem.

Representative Henry Cuellar, a Democrat whose congressional district includes a stretch of the Texas-Mexico border, said on CNN's "State of the Union" program that 48,000 people, including 9,700 children traveling without parents, were detained on the Texas border in May. "We should have been ready for this surge," he said. "The administration should have been ready ... They should have seen this coming a long time ago."

Idaho Representative Raul Labrador, a Republican, said the U.S. needs to take a strong stance against what is happening at border facilities.

"The thing that the administration needs to do is immediately deport these families, these children. I know it sounds harsh, I know it sounds difficult, but they're creating a crisis that's going to harm these children," he said on "Meet the Press."

Labrador added that the frustration building up is because the administration is doing nothing about border security.

(Reporting by Michael Flaherty; Editing by Jim Loney and Frances Kerry)