The D.C. government's summer jobs for youth program will offer jobs to 17,000 young people this summer, a reduction of 1,300 jobs from last year because of federal budget cuts, city officials said yesterday.

About 24,000 youngsters have registered for summer jobs, meaning about 7,000 will be left out unless a substantial number withdraw from the program during the summer, according to Don Tates, spokesman for the city's Department of Employment Services. The dropout rate has been as high as 12 percent in past years.

"It's tough for a lot of kids, but I think we're doing better than a lot of cities," Tates said. He said the city has allocated $5.2 million, the same amount as last summer, to hire 7,500 youngsters, while many cities have been forced to cut local contributions for summer jobs.

Tates said a $1.1 million cut in the city's Comprehensive Employment and Training Act (CETA) allocation has allowed the city only 8,500 CETA-funded jobs this summer, compared to 9,800 last year. "Next summer may be worse," he added. "We don't even know if there is going to be a CETA."

With unemployment increasing, the summer jobs are crucial for many families, Tates said, "This income is not as much supplemental as in past years. I have talked to parents who have been laid off, and this income is like a primary income for a family, almost. It only lasts seven weeks, but it's better than nothing."

Under the Summer Youth Employment Program, youngsters from ages 14 to 21 will be paid the federal minimum wage of $3.35 hourly for jobs ranging from 20 to 25 hours per week. In addition to city- and CETA-funded jobs, another 1,000 will be available in private businesses, mostly through the Greater Washington Board of Trade, Tates said.

Roughly one of every six young persons in the city from 14 to 21 will participate in the summer job program. There were 95,000 persons in that age group in 1980, according to the U.S. Census.