The Texas Republican suggested mobilizing the National Guard or amassing more Border Patrol agents as the caravan continues to make its way north. A United Nations spokesman said more than 7,000 migrants have joined the caravan, U.S. News and World Report reported. Their final destinations remain unclear, but Texas’ Rio Grande Valley has served as the main entry point for tens of thousands of Central Americans for nearly five years.

“I think this caravan is a serious threat. When you see thousands of people pledging to come violate U.S. law, to cross into this country illegally, we have to treat that seriously. We have to stop it,” Cruz told reporters after speaking at a Texas Oil and Gas Association forum in Houston. “Whether that means putting Border Patrol at the border to stop them or whether that means calling up the National Guard, which President Trump has done before, which President Bush has done before — that even President Obama called up the National Guard.”

President Donald Trump ordered National Guard units to the border in April in an effort to stop the flow of people entering the country illegally. But despite the deployment and an increase in interior enforcement, tens of thousands of migrants, the majority from Central America, have continued to cross the southern border seeking asylum. In summer 2014, former Gov. Rick Perry also deployed units to the border, which Gov. Greg Abbott kept in place after taking office.

Abbott’s office did not immediately respond to a comment about Cruz’s remarks Monday afternoon.

Last week, Mexican authorities said they had plans in the works to accommodate some of the migrants by offering visas or employment, CNN reported. According to media reports, the migrants entered the Mexican state of Chiapas, which borders Guatemala at the Suchiate River, over the weekend and Mexican officers used tear gas to stop the migrants after they reportedly broke through barricades on the bridge leading to Mexico. The migrants who could not enter Mexico at the port of entry instead swam across the river or paid people to ferry them across on rafts.

Trump tweeted on Monday that Mexican authorities were unable to stymie the flow of migrants, and suggested, without citing evidence, that “criminals and Middle Easterners” are mixed in with the travelers. “I have alerted Border Patrol and Military that this is a National [Emergency]. Must change laws!” he tweeted.

The president also reiterated his threat to cut off or reduce aid to Honduras, Guatemala and El Salvador, the countries of origin for most Central American migrants.

Patrick Svitek contributed to this story.