ST. PAUL — Minnesota officials announced Monday that schools will get about $636 million in back pay from state government soon thanks to an improved economy and a law putting them first in line for surplus tax collections.

Democratic Gov. Mark Dayton and leaders of the Democratic legislative majorities highlighted the payback as a sign the state is back on track and close to satisfying more than $2.8 billion in IOUs that piled up during lean times. The latest installment leaves about $238 million in outstanding debt to schools.

The payments to individual districts will go out on Oct. 26, state officials said. The per-district amounts are based on their enrollment and will be announced in a few weeks.

“The benefactors today are Minnesota kids, Minnesota schools and Minnesotans who value a balanced and honest budget,” said House Speaker Paul Thissen, DFL-Minneapolis.

But Republicans said they deserved the credit because the repayment is based on a budget that was adopted when they were in charge in 2011. That two-year budget expired on June 30, the trigger point for determining how much money was left to turn back to schools.

“Their plan was ‘Let’s rely on the GOP surpluses’ to pay back the schools. That plan worked,” Rep. Kelby Woodard, R-Belle Plaine, said of Democrats.

The reason the school spending decision is news now is that a law enacted this spring gave finance officials until Monday to figure out the pool of available money. Most of the amount bound for schools resulted from tax revenues that exceeded expectations. But another fraction is attributed to the state spending less than it expected on publicly subsidized health programs, property tax credits and agency operating budgets.

School leaders are sensitive about the payback. They fear that money previously committed to them will be perceived as a windfall. The IOUs were the result of the state holding back longer than usual on regular allowances sent to schools, an accounting trick that made the state’s own deficit appear smaller.

Many schools had to take out short-term loans or dip into rainy-day accounts to get by. Scott Croonquist, executive director of the Association of Metropolitan School Districts, said parents shouldn’t expect that schools will be able to add teachers, restore programs or make other investments with the settle-up payments.

“This does not result in any new money for schools,” Croonquist said. “Schools are just going to receive the amount they had coming sooner.”

The next checkpoint comes after Thanksgiving when finance officials publish a new economic forecast. If that shows another surplus, those dollars will also be shipped to schools first.

Dayton said he hopes Minnesota’s recovery will stay on course to quickly pay off the remaining debt, but he expressed worry about budget standoffs in Washington threatening to derail economic growth.

Republicans said they were skeptical Minnesota’s economy would churn out enough money for government to both repay the schools and allow for the repeal of some new taxes that even some legislative Democrats want scrapped.