More than 6,000 workers laid off from jobs in the District of Columbia are expected to qualify for extended unemployment compensation benefits under a provision of the new tax legislation signed recently by President Reagan.

City officials said the new law will permit eligible workers whose benefits have expired to receive six or eight weeks of further payments, depending upon future statistical calculations of the city's jobless rate.

Jobless workers covered by the D.C. unemployment compensation program, both city and suburban residents whose former jobs were with city-based employers, had been eligible to receive payments for up to 34 weeks. Then benefits ran out.

Under the new law, the added weeks of benefits will be paid to those whose benefit year ended on or after June 1, and who no longer qualify for regular benefits.

The D.C. Employment Services Department mailed notices Friday to the 6,000 persons whose records indicated they may qualify. Each notice indicated where and when the claimant should file the necessary application.

The amount of the weekly benefit will be the same as each claimant collected under the original jobless claim. The first payment will be for the week ending Sept. 18, with the program to conclude next March 31.

Unlike the regular jobless program, which is financed entirely through payments by employers, the cost of the extended program will be borne fully by the federal government.

Those with questions about the extended program should call 724-3877.