A wall along the U.S.-Mexico border, which local militia founder Tim Foley said drug traffickers are able to bypass within minutes, in Sasabe, Arizona, Jan. 12, 2016. Chris Riotta

It may seem like he just took office, but one of President Donald Trump's most controversial campaign promises could come to fruition before the end of 2019. U.S. Secretary of Homeland Security John Kelly told Fox News Wednesday that he hoped to finish construction on Trump's proposed wall along the United States-Mexico border "within the next two years."

"The wall will be built where it's needed first, and then it will be filled in. That's the way I look at it," Kelly said, adding that he thought "the funding will come relatively quickly."

Progress on, and debate around, the wall has been ratcheting up since Trump's Jan. 20 inauguration. The president issued an order last month calling for the executive branch to "secure the southern border of the United States through the immediate construction of a physical wall on the southern border, monitored and supported by adequate personnel so as to prevent illegal immigration, drug and human trafficking, and acts of terrorism."

He also started talking with Mexican President Enrique Peña Nieto about who would pay for the wall, sparking an argument that caused Peña Nieto to cancel a planned meeting with Trump. Trump has vowed Mexico will fund the construction, but Peña Nieto has rejected the claim amid rumors the White House could start taxing Mexican imports.

The cost of the wall has been estimated between $8 million and $15 billion, CNBC reported. Experts have suggested the wall could take between four and 16 years to make. But Kelly told Fox News the Trump administration was "looking at the money aspect" and working on the timeline.

One thing that could speed up construction is the 650 miles of metal barriers and fencing that already exists along the border, the Associated Press reported. It stands up to 26 feet tall and is reinforced by technology and border staffers — the latter of which Kelly acknowledged in his Fox News interview.

"Any discussion about the protection of our southwest border involves discussion of physical barriers but also of technological sensors, things like that," he said. "But it's a layered approach, and it’s got to be backed up by great men and women who are going to make sure that the wall is intact."