Congress has passed and sent to the White House emergency legislation that will extend until Sept. 30 the government's flexitime program that permits some employes to set their own hours and others to work four-day weeks at 10 hours a day.

The program, which covers about 20 percent of the Washington area's federal work force, was due to expire next Tuesday. Legislation that would have made the six-year flexitime experiment a permanent program has been bogged down in the Senate because of a dispute over the federal overtime law and proposals to establish a new (lower) minimum wage for teen-agers.

Late Wednesday evening the Senate approved the temporary emergency extension, sponsored by Sen. Ted Stevens (R-Alaska). An identical bill was introduced by Rep. Frank Wolf (R-Va.) and the House approved the emergency extension yesterday in a voice vote. President Reagan is expected to sign the bill during the weekend.

Because of the deadline, and earlier Senate deadlock over making flexitime permanent, many federal offices had already begun altering schedules for next week for employes who have been working four-day weeks. Federal law requires the payment of overtime after eight hours of work in one day. The flexitime experiment -- which has been extended to the end of this fiscal year -- permits federal agencies to waive the law and have people work 10-hour days.