The private border wall was back on track in New Mexico Thursday, after city officials withdrew their hold and said construction was in fact permitted.

Sunland Park Mayor Javier Perea had issued a dramatic cease-and-desist order earlier this week, saying We Build the Wall had begun construction without a permit, and complaining the 18-foot wall violated the city’s height restrictions.

But the city lifted its stop-work order Wednesday and construction began again at 6 a.m. Thursday, said Kris Kobach, general counsel for We Build the Wall.

He said they expect to finish construction of a half-mile wall, an access road and surveillance lights by Saturday.

“The stop work order only delayed us for 36 hours,” he said.

The private wall has upended the border debate, creating new options for fulfilling President Trump’s most prominent campaign promise without having to rely on funding from Congress.

We Build the Wall founder Brian Kolfage held a press conference in New Mexico Thursday to announce 10 more projects he said are in the pipeline.

Mr. Perea, in announcing the stop-work order on Tuesday, had suggested a lengthy months-long process, including a court battle, to get permits done.

On Thursday he backed off — though he still blamed We Build the Wall for the delay, and said the group may face fines for beginning construction without having all its permits fully ready.

“If they had done their due diligence ahead of time it would have given the staff enough time to address the concerns in an appropriate manner,” the mayor said, according to the El Paso Times. “We will continue to ensure that they are meeting all city ordinances for the time being.”

He’d said earlier this week that the wall violated a 6-foot limit on fencing. He’d also suggested federal agencies would have a stake in construction on the border.

But Mr. Kobach said the mayor was “poorly informed.”

“That portion of the city code has nothing to do with property like American Eagle Brick,” Mr. Kobach said.

American Eagle Brick Company owns the land on which the fencing is being constructed. The land has been in private hands since the 1880s, or before New Mexico was a state, and before the 1907 declaration by President Theodore Roosevelt creating a 60-foot buffer zone at the border.

We Build the Wall raised money for the wall through GoFundMe, an online crowdfunding site.

The new wall begins at the Rio Grande and runs up to the lower elevations of Mount Cristo Rey. There is a wall on the Texas side of the river, but it didn’t pick up on the New Mexico side.

Two parking lots, one on the Mexican side and one on the U.S. side, with naught but a ditch to separate them, offered a convenient staging point for would-be migrants.

Mr. Kobach says agents have told him perhaps 100 migrants a night crossed through the gap — but the bigger problem is that when they crossed, they distracted agents, and drug smugglers would run drugs through elsewhere in the gap.

A typical night could see in excess of $100,000 worth of drugs funneled through the gap, Mr. Kobach said.

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