WASHINGTON — Unemployment rates fell in 29 states in August and held steady in 11 as hiring remained solid nationwide. Falling oil and coal prices continued to take a toll on energy-producing states.

The Labor Department said Friday that rates rose in the remaining 10 states. Employers added jobs in 32 states and shed them in 18.

Oil prices that are sharply lower than a year ago contributed to job losses and higher unemployment in several states, including Alaska, North Dakota, and Texas. And falling demand for coal has devastated West Virginia, which has the nation’s highest unemployment rate at 7.6 percent. That is up from 7.5 percent in July.

South Dakota reported the largest percentage loss of jobs last month. Texas, meanwhile, shed 13,700 positions, the most of any state except New York, which lost the same amount.

Nationwide, employers added 173,000 jobs in August, while the national unemployment rate fell to 5.1 percent from 5.3 percent.

The state unemployment report comes a day after the Federal Reserve decided against raising short-term interest rates, citing threats to the U.S. economy from weak growth in China and the persistence of very low inflation.

Tara Sinclair, chief economist for the jobs website Indeed, said the state data supports the Fed’s decision to delay. Ongoing lower rates could help spur further hiring.

Sinclair says that 36 states still have higher unemployment rates than they did before the Great Recession began in December 2007. And 14 have rates much higher than the 5 percent that the Fed says is consistent with a healthy economy, including Alabama, Arizona, California and North Carolina.

“These results are in line with the Fed’s holding off on an interest rate hike yesterday,” Sinclair said.

Unemployment in California, the largest state by population, remains elevated at 6.1 percent, though that is down sharply from 7.4 percent a year ago. Alaska’s unemployment rate is 6.6 percent, down only modestly from 6.9 percent a year ago.

Nebraska continued as the state with the nation’s lowest jobless rate, though it rose to 2.8 percent from 2.7 percent the previous month. North Dakota has the second-lowest, at 2.9 percent, down from 3 percent the previous month.

Still, North Dakota, which has benefited from a boom in oil and gas drilling, is one of three states to lose jobs in the past year. The other two are West Virginia and Alaska.

The states with the biggest job gains in August were California, with 36,200; Florida, with 19,600; and Ohio, with 14,600.