O’Rourke, who narrowly lost a 2018 bid for a U.S. Senate seat in Texas, accused Trump of stoking “false fear” about immigrants and telling “lies” about his hometown El Paso, which Trump said was a dangerous place before it had a border fence.
“Here is one of the safest cities in the United States of America, safe not because of walls but in spite of walls,” O’Rourke told a crowd of several thousand supporters, many waving “Beto 2020” signs and wearing “Immigrants Make America Great” baseball caps.
Trump is in El Paso to argue for a wall he says can protect Americans from violent criminals, drugs and a “tremendous onslaught” of migrant caravans.
A sea of Trump supporters in red caps waited for the arrival of the president at the El Paso County Coliseum under giant “Finish the Wall banners.”
The rally was due to be his first direct clash with a potential 2020 rival, albeit on separate stages in venues about 200 yards apart.
The rallies coincide with talks in Washington to reach a border security deal and avert another government shutdown.
One of the negotiators, Republican Senator Richard Shelby, told reporters late on Monday that an “agreement in principle” had been reached but did not give any details.
EL PASO: “LOW ON CRIME”
In his State of the Union speech, Trump said the border fence separating El Paso from Mexico reduced the city’s high crime rate.
El Paso’s Republican mayor, Dee Margo, said the city had been safe for years before the wall was built.
“We were, I think, the No. 2 or No. 3 safest city before the fence went up and we progressed into No. 1,” he told Fox News. “We were significantly low on crime to begin with and always have been.”
O’Rourke told Oprah Winfrey last week he would make a final decision about running for president by the end of the month.
He declined to discuss a potential run on Monday. “I’m following the community’s lead tonight, no less, no more,” he said on a conference call with reporters.
Reporting by Tim Reid in El Paso, additional reporting by Steve Holland and Tim Ahmann in Washington; Writing by Andrew Hay; Editing by Colleen Jenkins, Bill Tarrant and Sonya Hepinstall