The National Weather Service notified lawmakers Thursday that it plans to furlough up to 5,000 employees for 13 days between July and September if Congress and the agency cannot find $36 million to cover its budget deficit.

Weather Service officials acknowledged to legislators, as well as the union, that requiring employees to take unpaid leave could disrupt critical weather operations at the peak of the hurricane season.

But with labor costs of $2 million a day, the Weather Service cannot pay its employees through the end of the fiscal year in September without a solution to a problem of its own making. An internal investigation concluded that for years, the agency reallocated millions of dollars that Congress approved for other projects to pay employees.

The investigation, disclosed last month, prompted the retirement of the Weather Service’s director, John L. “Jack” Hayes, after the replacement of its chief financial officer.

Weather Service officials have stopped the practice of reallocating funds once the investigation was underway.

Officials at the National Oceanic and Atmospheric Administration, which directs the service, have declined to say publicly why the practice went on and who authorized it. They have asked Congress to cover the gap through the fiscal year.

But lawmakers who oversee the Weather Service’s budget have said they will not consider the request until they know more about what happened.

The House Appropriations panel that oversees NOAA and the Weather Service scheduled a June 21 hearing.

“If faced with this difficult situation, [the Weather Service] would work to prioritize resources and staff for mission-critical operations,” agency officials wrote to the National Weather Service Employees Organization about possible furloughs. “Weather operations would likely be affected.”

Furloughs “would also reduce staff or potentially close weather forecast offices and river forecast centers during the time of year when there are significant hurricanes, flash floods, extreme heat and forest fires,” officials wrote.

Union President Dan Sobien called the furlough notice a negotiating tactic by NOAA to prod action from Congress and the Commerce Department, which began talks last week to find a solution.

He said the effects of furloughs would be crippling, from emptying forecasting offices to cutting vital meteorological guidance to air traffic controllers at airports.

“You can’t stop hurricanes or tornadoes because we’re furloughed,” he said.

The union has 15 days to respond to the announcement. While it cannot stop the Weather Service from mandating unpaid time off, it can negotiate the terms.

NOAA spokesman Scott Smullen said the agency “is committed to doing everything within its authority to avoid furloughs.”

Sen. Barbara A. Mikulski (D-Md.), chairman of the Appropriations subcommittee on commerce, justice, science and related agencies, said Thursday that she opposes furloughs. “I am on the side of the men and women of the Weather Service and the American people who depend on their forecasts and warnings,” she said. She said she is working with her Republican colleagues “to get all the facts so we can agree to a new plan to prevent furloughs in the short term.”

Rep. Paul C. Broun (R-Ga), chairman of the House Science, Space and Technology subcommittee on investigations and oversight, said his staff has repeatedly asked NOAA to see a copy of the investigation. NOAA officials said it had been delivered Wednesday.

“Either NOAA turned a blind eye to this deficit, or they were asleep at the wheel,” Broun said in a statement.

The Weather Service staffs 122 forecast offices throughout the country — including Guam and Puerto Rico — and key centers such as the National Hurricane Center in Miami and the Storm Prediction Center in Norman, Okla.

The offices issue watches and warnings for violent weather including severe thunderstorms, tornadoes, flash flooding and hurricanes.

Employees say they fear that furloughs coinciding with severe thunderstorm and hurricane seasons could compromise the quality and timeliness of information provided about these hazards.

NOAA officials have said there is no evidence of fraud or personal gain from the misdirected money. But the investigation, prompted by anonymous complaints in 2010 and 2011, concluded that senior Weather Service staff members operated “outside the bounds of acceptable financial management.”