The number of working oil rigs in North Dakota fell 13 percent in the past month as more drillers called it quits amid falling oil prices, state officials said Wednesday.

The 158 rigs still working in the oil fields — down 23 from December — are concentrated in the four most productive counties at the core of the Williston Basin of western North Dakota, said Lynn Helms, director of the state Department of Mineral Resources.

“Rigs outside the core area are going to be hard to find,” Helms said during his monthly industry update, called the Director’s Cut. “There is almost no place outside the core area where today’s oil prices support drilling.”

The deflating oil boom in North Dakota mirrors conditions across the oil industry. With oil prices down 58 percent over the past six months, the U.S. Energy Department on Tuesday predicted that oil production in the nation’s shale plays would decline later this year.

Helms also projected that North Dakota’s drilling could decline further, to as low as 120 rigs later this year if prices stay low. That’s potentially below the level needed to keep North Dakota’s oil output from dropping below the current 1.2 million barrels per day.

Overall, drilling is down 28 percent from the peak in October 2010, but some counties saw declines as high as 62 percent, he said.

The price of crude oil at North Dakota wellheads fell this week to $29.25, the lowest since 2008, Helms said. At that price, only wells in the two most bountiful counties, Dunn and McKenzie, are above the break-even point, according to state data.

Across the oil industry, 39 companies have cut capital spending budgets more than 20 percent as oil prices have plunged, according to a Bloomberg analysis. Oasis Petroleum, a leading Bakken producer, recently said it would reduce rigs from 16 to six by March. American Eagle Energy, a smaller player in the Bakken, said Dec. 31 it would suspend all drilling in 2015 until crude oil prices rise.

The fall in prices has big implications for North Dakota, which gets about 11 percent in taxes from each barrel of production. Under the tax law, the rate drops when oil sinks below certain price targets, and that appears to be affecting drillers’ next moves.

Helms said that a record 775 wells are drilled, but not producing because owners are waiting to do the hydraulic fracturing, a process that injects water, chemicals and sand to get oil flowing. Some of the holdup may be caused by cold weather, when fracking is difficult, he said.

But Helms said many drillers are watching oil prices to see if they slip below trigger points for lower tax rates. If the triggers kick in, any wells completed after that would save about $170,000 each on taxes over 18 months, said North Dakota Tax Commissioner Ryan Rauschenberger, who also spoke on the conference call with reporters.