Trump called O'Rourke, who was headlining a counter-rally in El Paso at the same time as the presidential speech, "a young man who has got very little going for himself except he's got a great first name". He cited the number of people who have died trying to enter the United States since 650 miles of fencing went up along the southern border over the past decade.

Media captionOther presidents got money for a border barrier - why not Trump? O'Rourke thinks this fencing is not only unnecessary but harmful, because it makes it more hard for people from Mexico and Central America to enter the United States. He challenged us. We have, say, 35,000 people tonight, and he has, say, 200 people, 300 people, ' Trump said. "Just so you know, we're building the wall anyway", he said to raucous applause, underneath "Finish The Wall" banners.

"I don't think you're going to see a shutdown", Trump said, but he added: "If you did have it, it's the Democrats' fault".

"Across the street, one of his potential 2020 rivals - former Texas Congressman and El Paso native Beto O'Rourke - held a competing rally that drew thousands of people".

Democrat Beto O'Rourke told a hometown El Paso crowd that it's time to "show the country that there is nothing to be afraid of when it comes to the U.S. -Mexico border". The rally was dedicated to advocating for the border wall between the US and Mexico and didn't do much to mend the relationship between officials in the city and the president.

Trump said he heard about progress in the talks just before he took the stage, but he too did not discuss details. "I could've stayed out there and listened, or I could have come out to the people of El Paso, and Texas, I chose you", Trump said.

President Donald Trump acknowledged the breakthrough in negotiations at his rally for border security in El Paso last night, but gave no clear signal he'll support it.

As for O'Rourke, NBC News estimated that there were 7,000 and 8,000 people at his rally and march. At various points during his own rally, Trump claimed that 69,000 people had RSVP'd and that fire marshals allowed 10,000 people in with "tens of thousands" still watching outside.

O'Rourke directly took on Trump over border security and Trump's desire for a wall or other physical barrier.

"We know that walls do not save lives".

In a taped interview with Oprah Winfrey in NY, O'Rourke, 46, appeared to be leaning toward a 2020 campaign for the White House but said he would make his decision after consulting his wife and three children.

"We have a line that's very long already", Trump said of his El Paso rally. He told them the idea of Clinton being convicted of crimes - apparently related to her use of a private email server as secretary of state - as looking like a better and better idea.

He repeated his warnings about drugs and human traffickers coming over the border, and argued Democratic attempts to bolster security at ports of entry won't help. "It's not doing the trick", he said a day after Democrat and Republican negotiators struck a deal to avert a shutdown ahead of Friday, when funding for some federal agencies is due to run out. During the 2018 midterm elections, pollsters advised that it was more important to reintroduce the party's views on key economic issues than to attack the president. He said he will not sign anything into law that would do away with or cut back on the number of beds in ICE detention centers.