About 4,000 employees of the Federal Aviation Administration, including almost 1,000 who live in the Washington region, would receive back pay for the two-week partial shutdown of the agency under a bill introduced in the House on Tuesday.

Restoration of the lost pay has been expected but requires congressional action. With Congress away until after Labor Day, it would be September before the workers see the money.

“For the past two weeks it was important to get these workers back on the job,” Rep. Frank A. LoBiondo (R-N.J.) said in a statement. “Now my focus is to get them back pay and to ensure this avoidable situation never happens again.”

LoBiondo introduced a bill that would tap into the federal Aviation Trust Fund to pay the 4,000 people who were furloughed from July 23 to Aug. 5 after Congress deadlocked on extending FAA funding authorization. An estimated $350  million in airline ticket-tax revenue that would have flowed into the trust fund was lost during the impasse.

LoBiondo’s southern New Jersey district is the location of the FAA Technical Center, from which about 650 workers were furloughed. The bill does not provide back pay for tens of thousands of contract construction workers who were laid off when FAA funding expired.

LoBiondo received bipartisan support for the bill, with Transportation Committee Chairman John L. Mica (R-Fla.) and Reps. Peter T. King (R-N.Y.), Lynn A. Westmoreland (R-Ga.), Gerald E. Connolly (D-Va.) and Jon Runyan (R-N.J.) signing on.

The FAA funding bill, which faltered before winning Senate approval Aug. 4, marked the 21st time current funding has been extended since the last long-term FAA authorization expired in 2007.

Unless Congress can agree on long-term bills passed this year by the House and Senate, the prospect of extending funding for the 22nd time will arrive Sept. 16. Most members of Congress headed home last week, and it was unclear whether they left behind staff members designated to iron out differences between the two bills.

“The House and Senate must now work to ensure the end of a 41 / 2-year delay in passing a long-term FAA bill,” Mica said Tuesday.

The Senate, which has bridled at the fact that the House has yet to name a conference committee to meet with its own, fired back with a letter signed by Senate Majority Leader Harry M. Reid (Nev.) and five other Senate Democrats.

Addressed to House Speaker John A. Boehner (R-Ohio), it made reference to public remarks by House Republicans last week.

“Public statements from you and Chairman John Mica say that you are ‘willing to use every tool at your disposal’ to negotiate a final FAA bill, yet one tool you have so far been unwilling to use is the normal legislative process,” the senators wrote.

“More than 120 days ago, a bipartisan group of senators was appointed to the conference committee between the Senate and House FAA bills. These senators are eager to negotiate in earnest, but their House counterparts have not been named more than four months after the House passed their FAA bill.”