An order signed by President Trump to boost unemployed workers’ weekly benefits will not deliver any new aid to South Dakota, where Republican Gov. Kristi L. Noem appeared to become the first state leader to decline the heightened federal support.

Noem, one of Trump’s most vocal allies, said South Dakota did not need to accept the additional federal jobless aid because workers in the state are being rehired, and its economy is on the mend, even as the coronavirus pandemic continues to rage across the United States.

Under Trump’s order, the federal government aims to divert billions of dollars in federal disaster assistance to out-of-work Americans, adding at least $300 more to their weekly benefit amounts — and more if states put up additional financing of their own. The program is supposed to offer a brief, temporary respite after the $600 payments that millions of workers had received regularly expired at the end of July.

But Trump’s order has set off a scramble among states, which have faulted it as financially and technically unworkable in the absence of a more lasting solution from Congress. Amid the turmoil, Noem said Friday she opted to forgo the money in South Dakota entirely, claiming the state had recovered roughly 80 percent of its pandemic-related job losses.

“My administration is very grateful for the additional flexibility that this effort would have provided, but South Dakota is in the fortunate position of not needing to accept it,” Noem said in a statement, which noted the state never shut down in response to an outbreak.

Labor economists and unemployment experts said the reality is far more complicated in South Dakota, where total confirmed coronavirus cases since February recently surpassed 10,000. In citing progress, Noem this week pointed to the fact that the Mount Rushmore State boasts the country’s lowest insured jobless rate at roughly 3.5 percent. But the figure measures those who receive benefits compared with the total labor force. Meanwhile, South Dakota’s overall unemployment rate is roughly 7.2 percent, a gap in indicators that may reflect the reality that some people out of work are having a hard time obtaining sufficient safety-net support.

Roughly 20,000 people in the state are currently collecting jobless benefits, according to recent federal data that tracks both traditional unemployment insurance as well as the new pandemic-related aid authorized by Congress. But Michele Evermore, a senior policy analyst at the National Employment Law Center, said the number in some ways is irrelevant: “If you’re an unemployed person in South Dakota, it’s not going to matter to you there aren’t a lot of unemployed people,” she said.

In the meantime, dozens of states nationwide say they are still awaiting for critical guidance from the Trump administration over the president’s order signed last weekend. States including Arizona, Colorado, Florida, Louisiana, North Carolina and West Virginia have signaled in recent days they are likely to try to get the limited, additional payments to their out-of-work residents, but some have warned about serious obstacles that threaten to result in significant delays.

For one thing, the president has touted that jobless Americans could see a $400 boost to their weekly checks. But the amount is actually contingent on states supplying a quarter of the funds on their own dime, a burden some governors have said they simply cannot bear during the worst economic crisis since the Great Depression.

Instead, many states are likely only to be able to offer $300 to their workers, prompting widespread consternation that the amount is insufficient. It could also take weeks for states to upgrade their computer systems and get payments out to families in need, creating the potential for the same technological breakdowns that prevented millions of Americans from obtaining benefits swiftly when the coronavirus pandemic began earlier this spring.

The difficulties drew a sharp rebuke Friday from Pennsylvania Gov. Tom Wolf (D), who lamented in a letter that the president’s approach essentially forbade states from trying to pay out the additional sums in unemployment benefits using their existing systems. The deficiencies, he said, could leave people with the impression they have been “shorted” by their states, when it is not their local governments’ fault.

“This is a convoluted and short-lived proposal that will delay payments to unemployed Pennsylvanians and create unnecessary and costly administrative burdens for the states who must administer the funds,” he said.