White House spokesperson Sean Spicer says "one way or another, Mexico will pay for it."
US President Donald Trump has said he expects to begin building a wall on the border with Mexico within months.
The President said in an interview with ABC News that planning for it was well under way - and repeated his pledge that Mexico will pay for it.
Mr Trump told the television network that while US taxpayers would initially fund it, Mexico would ultimately foot the bill, with reimbursement negotiations starting "relatively soon."
"There will be a payment, it will be in a form, perhaps a complicated form," Mr Trump said.
White House Press Secretary Sean Spicer said the measure was a "common sense first step" and added: "One way or another, Mexico will pay for it."
Mexican President Enrique Pena Nieto, who insists his country will do no such thing, is set to meet Mr Trump in the White House next week.
Mr Trump would need to get approval from Congress for any new funding for the wall - with costs estimated at £5.2m ($6.5m) per mile for a single-layer fence by the Government Accountability Office.
Mr Trump, is expected to sign an executive order enabling construction of the wall later on Wednesday, as he begins an immigration crackdown.
As well as taking the first steps towards building what could eventually become a 2,000-mile barrier stretching across the southern US, Mr Trump is also expected to target so-called "sanctuary cities," where local officials refuse to hand over illegal immigrants for deportation.
Restricting access to the US for refugees and some visa holders from Syria, Iraq, Iran, Libya, Somalia, Sudan and Yemen is also anticipated to form part of the crackdown.
The limits on refugees could include a ban lasting months on admissions from all countries until the State Department and the Department of Homeland Security can increase the intensity of the vetting process.