Mr Trump said the price would drop "way down" once he became involved in the planning process, apparently suggesting the US would foot at least part of the bill.
The President has previously insisted Mexico will pay for work on the 2,000-mile-long "impassable physical barrier". Mexico has refused to fund it.
Fact checkers and engineers have estimated the cost of building the wall will far exceed the $12bn (£9.6bn) estimate given by Mr Trump.
According to a leaked Department of Homeland Security report, the barrier could cost as much as $21bn and take more than three years to construct.
Some 650 miles of fencing already in place has come at an expense of $7bn and Mr Trump's plans require extending the barrier into increasingly remote and mountainous regions, which raises the building costs significantly.
Repeating his promise that Mexico would pay for it, the President signed an executive order directing construction of the wall in early February, .
The next day, White House press secretary Sean Spicer said the wall would be funded through placing a 20 per cent tax on all imports from Mexico, a move that would likely hit US consumers.
Yet White House chief of staff Reince Priebus later said the tax was only one of a "buffet of options", adding to a statement made the previous evening by House Speaker Paul Ryan, who said there were "various ways" Mexico could reimburse the US.
On Friday there were reports that hundreds of undocumented immigrants were arrested in at least four states over the course of five days, sparking concern among immigration advocates and families.
David Marin, director of enforcement and removal for the Los Angeles field office of US Immigration and Customs Enforcement, described the operation as an "enforcement surge".
Mr Trump has expanded the powers of immigration agents since entering office. Some analysts say that up to eight million illegal immigrants now face deportation.
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