WASHINGTON — Up to 4,800 U.S. National Weather Service employees could face 13 days of furloughs if Congress does not soon sign off on a plan to fill a looming budget gap, the administration of President Barack Obama is warning.

In a notice to the union representing weather service employees, the agency said it lacks $26 million needed to cover payroll through the end of the fiscal year.

The weather service’s parent agency, the Commerce Department, in May asked Congress to “reprogram” money from other accounts to cover that cost. But lawmakers are balking, saying they want more information after an investigation found that weather service managers in 2010 and 2011 shifted money among different accounts without congressional approval.

To avoid the furloughs, the needed funds must be in place in the next few weeks, the agency told the National Weather Service Employees Organization in the June 1 notice, which was posted on the union’s website. If furloughs began in mid-July, each employee would have to take two to three days off each pay period for the rest of the fiscal year, according to the weather service.

But Richard Hirn, a lobbyist for the union, said he is optimistic that Congress and the Obama administration will work something out. Key lawmakers vowed action.

“We cannot allow furloughs because of inept bureaucracy,” said Sen. Barbara Mikulski (D-Md.), who chairs the appropriations subcommittee that drafts the weather service’s budget. In a June 8 statement, Mikulski said she is working with the panel’s top Republican, Sen. Kay Bailey Hutchison of Texas, to head off furloughs in the short term while devising a long-term strategy to “right the Weather Service’s financial ship.”

A House appropriations panel has scheduled a June 21 hearing on weather service funding issues, a spokesman for the chairman, Rep. Frank Wolf (R-Va.), said.

The National Oceanic and Atmospheric Administration (NOAA), a Commerce Department agency that includes the weather service, “is committed to doing everything within its authority to avoid furloughs,” spokesman Scott Smullen said. The notice to the union is not a formal trigger of the furlough process, he said.

Meanwhile, NOAA managers completed a 60-page investigative report into the alleged unapproved fund transfers at the weather service, but it has not released the report.

Some insiders and experts say the investigation’s findings mask a deeper problem: Agency managers were trying to make do with too little money.

For years, the weather service has suffered a “structural deficit” as its budget failed to keep pace with increasing expenses, particularly for salaries, Hirn said.

Although the transfers were illegal, “this was simply done in order to keep the operation going because the weather service viewed that there was no other alternative,” said Elbert “Joe” Friday, a former director of the agency who is now professor emeritus at the University of Oklahoma’s meteorology department. “I don’t think there was any nefarious intent at all.”

Bill Proenza, the weather service’s regional administrator for the Southern United States, agreed. While not familiar with details of the transfers — which were done without required congressional approval —Proenza said that the agency struggles to keep up with its around-the-clock mission to protect human life.

“The budget request that goes through has been barely adequate,” he said.

But in the past, seeking congressional permission to move money among different accounts would have been an admission that a budget shortfall existed, Hirn said. As a result, he said, leaders of the weather service and NOAA “covered up.”

In a memo in late May summarizing the inquiry’s findings, NOAA Administrator Jane Lubchenco said weather service employees used “a variety of financial mechanisms” to free up money from other accounts for the agency’s local forecast offices during 2010 and 2011.

As remedies, Lubchenco outlined a dozen measures, including more oversight of weather service finances and an outside audit to determine whether there is any merit to the claims of a structural deficit.

On May 29, the day after the findings became public, the weather service’s director, Jack Hayes, retired. Hayes, who told his staff that he had been contemplating retirement for some time, did not reply to an interview request relayed through Hirn.

Dust-ups about the weather service’s budget are not new. In 2007, the service’s director and deputy director resigned after Proenza, who headed the National Hurricane Center at the time, complained of cuts to research funding while NOAA was spending money on a 200th anniversary celebration.