NACO, Arizona — The estimates of President Trump’s proposed border wall run anywhere from $8 million to $25 million a mile, White House budget director Mick Mulvaney said in a radio interview Monday — though he said no decisions have been made on exactly what the wall will look like.

Mr. Mulvaney, speaking on the “Hugh Hewitt Show,” said the White House will ask for some money in the next couple of weeks but won’t know the details of the cost and construction until it prepares its 2019 budget, which won’t be for another year.

The director also raised the possibility that much of the new barrier will be fencing, rather than a complete concrete wall stretching the 1,950 miles of the U.S.-Mexico border.

“It just depends on the kind of wall that you want to build, and I don’t think we’ve settled yet on the actual construction,” Mr. Mulvaney said. “You can do steel, you could do concrete, you can do a combination of concrete and steel. You can supplement it with different types of technologies and so forth. So it sort of depends on what you want to build.”

He also said the Office of Management and Budget is looking to match the type of fence or wall with the terrain.

Mr. Trump made building a wall along the southwest border a major theme of his campaign. But he gave conflicting details. He did, however, insist it would be a wall, not a fence.

Some 654 miles of the border currently have a barrier, though just 354 miles are covered by a substantive fence that is designed to keep out people and vehicles. Another 300 miles are covered by vehicle barriers that are easy for those on foot to step over or slide under.

The Border Patrol has experimented with different styles of fence and has concluded that those with alternating slats, which allow some visibility through to the Mexican side, are the most effective and the safest. Earlier versions with solid “landing mat” plates proved to be dangerous to agents because they allowed those on the Mexican side to wait in ambush and throw rocks over the fence with impunity.

Border Patrol agents said they used to be anxious when they got close to the wall because of the threat of being bombarded. But the new style of fencing has dramatically reduced the number of assaults on agents, they said.

The cost of Mr. Trump’s wall has been a major source of contention. Democrats say that building a barrier along the southwestern border would be a waste of money.

A recent round of fence building in Naco, Arizona, cost $6 million per mile, according to U.S. Customs and Border Protection figures provided to the Government Accountability Office.

But the White House is looking at figures higher than that, according to what Mr. Mulvaney told Mr. Hewitt on Monday.

“I’ve got, I don’t know, six or seven different papers on my desk. I’ve got one that goes, starts at $8 million per mile. It goes up to about $25 million per mile. So again, it just depends on, when you’re talking about across 2,000 miles or so, what you decide to build in what areas,” he said.

The debate about what fencing or wall is appropriate for which areas has raged for years. Congress in 2006 passed the Secure Fence Act, calling for 850 miles of a two-layer fence.

But that was reduced to just 700 miles of whatever type of barrier the Homeland Security Department deems necessary.

The department is 46 miles short of that goal.

In 2013, the Senate approved a bill that would have demanded an additional 350 miles of pedestrian fencing. That bill was approved with the support of every Democrat and about a third of Republicans.

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