Across the country, states, school districts and transportation authorities may end up spending hundreds of thousands — even millions — of dollars more on interest payments in another byproduct of the automatic spending cuts that kicked in this month.

A D.C. official said that the city — which sold about $1 billion in bonds to finance projects ranging from Metrorail improvements to school modernization — could end up paying bond holders about $1 million more in interest during the current fiscal year.

The costs stem from a federal initiative, created as part of the stimulus program, that helped thousands of local governments finance construction projects such as rail extensions, school renovations and bridge reconstructions.

To encourage such spending, the federal government said it would pay 35 percent of the interest owed to bondholders by the local governments and authorities that issued the bonds. For cash-strapped cities, schools and counties, the federal program allowed them to stretch their spending a little further.

But sequestration has altered that equation. Those subsidies are now being reduced by $171 million, leaving local officials to cover the sizable portion that had been covered by the federal government.

The impact varies. California, which sold $13.8 billion in Build America Bonds, the most of any entity, will be responsible for about $12 million in additional interest payments, said Tom Dresslar, spokesman for state Treasurer Bill Lockyer. The number may seem daunting, but it is a small percentage of the $95 billion state budget, Dresslar said.

That’s not to say that the added expense — even at smaller institutions — necessarily sits well with officials.

At the University of Virginia, where officials used proceeds from the bonds to fund renovations to student housing, the university bookstore and hospital, reserve funds will cover the gap.

“It’s not significant, but it is money we’d rather not pull out,” said James S. Matteo, an assistant vice president at the university, which will see a $380,000 increase in interest payments to bondholders.

In the District, officials anticipated that there might be a shift in the reimbursement rate, said Malik K. Muhammad of the D.C. Office of Finance and Treasury. That was factored into their budget planning, but the extra cost is still unwelcome.

“Every million is important because it could be used to subsidize something else,” Muhammad said.

The Metropolitan Washington Airports Authority, which sold $550 million in bonds to finance construction of the first phase of the Dulles Metrorail extension, will owe just over $637,000 in additional interest payments if no action is taken to restore the full subsidy, MWAA spokesman Rob Yingling said. But the reduced subsidy is likely to have a minimal effect on the authority’s bottom line, said Andrew Rountree, MWAA’s chief financial officer, and it is not expected to affect rates on the Dulles Toll Road, which is funding more than half the cost of the rail extension.

“In relation to the total debt, it’s not a lot of money,” Rountree said. “But anytime you’re talking thousands of dollars, that’s still a lot of money to have to incur for a program we thought would be appropriately supported by the federal government.”