Trump was speaking at a conference of US sheriffs and police chiefs on Wednesday. Democrats in Congress are refusing to provide the necessary funding. The President is under pressure to reach a deal with Congress to avoid another government shutdown.
Trump insisted: “We will get the job done.
“The wall is very, very on its way. It’s happening as we speak.
“We’re building as we speak in the most desperate areas.”
He was addressing the Major County Sheriffs and Major Cities Chiefs Association Joint Conference in Washington.
Trump went on to emphasise how hard the wall, when finished, would be to cross illegally.
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To some laughter from the crowd he said: “You’re going to have to be in extremely good shape to get over this one.
“They would be able to climb Mount Everest a lot easier, I think.”
However on Tuesday Fox News reporter Shepard Smith shot down Trump’s claim that construction of the wall has already started.
He commented: “That’s incorrect.
“He’s been saying it for a while now but it’s simply not true.
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“The facts are these: workers have replaced and repaired sections of the existing wall and fences, but so far they have not built anything new.”
Trump is under pressure to accept a deal from Democrats in Congress, in order to prevent the third government shutdown of his presidency.
However any deal is likely to provide only a fraction of the $5.7bn (£4.4bn) funding Trump wants for the wall.
The US government experienced a partial shutdown for 35 days from December 22, the longest in its history.
The shutdown began when Trump refused to approve a Congressional finance bill unless it included border wall funding, which Democrats refused to provide.