The Texas border city of El Paso became a focal point of the nation's contentious debate over immigration Monday night, as President Trump and former Democratic Congressman Beto O'Rourke, a potential 2020 challenger, held dueling rallies to tout completely different immigration agendas.

In his first "Make America Great Again" campaign rally of 2019, the president again argued for the construction of a wall along the U.S.-Mexico border by railing against illegal immigration and falsely linking undocumented immigrants to disproportionate criminality. He accused Democrats of endorsing "open borders" and criticized the "far-left" for efforts to defund or abolish Immigration and Customs Enforcement (ICE).

"Illegal immigration hurts all Americans — including millions of legal immigrants — by driving down wages, draining public resources and claiming countless innocent lives," Mr. Trump said, adding later, "We will never abolish ICE."

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Encouraged by boisterous chants of "build the wall!" and "USA!" the president also vowed to never sign legislation that "forces the mass release of violent criminals," slamming Democrats for wanting to cap the number of beds in ICE detention centers — the source of a recent impasse in budget negotiations in Congress.

It is unclear if he will support a budget agreement to avert another government shutdown that was brokered on Capitol Hill minutes before he took the stage. A congressional aide told CBS News the legislation includes $1.375 billion in funding for physical barriers and a decrease of the overall number of ICE detention beds to 40,520, down from the current 49,057 level. In an interview recorded before the rally, the president told Fox News' Laura Ingraham he was briefed on the deal "very quickly."

"A lot of things have changed. And we'll see what happens," he told Ingraham.

President Trump speaks during a rally at the El Paso County Coliseum on Mon., Feb. 11, 2019, in El Paso, Texas. Mr. Trump continues his campaign for a wall to be built along the border as the Democrats in Congress are asking for other border security measures. Getty

After touting "the hottest economy on Earth" and his administrations's funding for the military, the president mocked O'Rourke, who's mulling a 2020 presidential bid, for hosting a counter rally blocks away, bragging that his event drew a larger crowd.

Succeeding an opening act that included a mariachi band, O'Rourke denounced the president's hardline immigration agenda, provoking multiple chants of "¡Sí se puede!" — or "Yes, we can!" in English. The Texas Democrat said a border wall would be ineffective and make the journey north for Central American families fleeing widespread poverty and violence even more perilous.

"We know that walls do not save lives. Walls end lives," he added. "In the last 10 years, more than 4,000 children women and men have died trying to come to this country to work jobs that no one will take, to be with a family member, to flee horrific violence, brutality and death."

Again rebuking the president, O'Rourke called El Paso "one of the safest cities in the United States of America."

"We have the chance to tell him and the country: immigrants commit crimes, including violent crimes, at a lower rate than Americans born in this country," O'Rourke said, referring to Mr. Trump. "El Paso has been the safest city in the U.S. not in spite of being a city of immigrants but because we are city of immigrants."

On Monday, Mr. Trump again falsely cited El Paso as an example of a city where the construction of a wall bolstered security and curtailed crime rates. His claims have been widely rebuffed, including by El Paso's Republican mayor Dee Margo.

A report by Politifact noted the city's violent crime rate "was significantly lower than the average for all localities of a similar size" for every year between 1985 and 2014. El Paso's had an estimated population of 683,577 people in 2017, according to the U.S. Census Bureau.

During his raucous rally, Mr. Trump also denounced the "Green New Deal" recently proposed by progressive Democrats and again seized on controversial remarks by Virginia's beleaguered Democratic Gov. Ralph Northam to urge lawmakers to pass legislation that bans late-term abortion.