With registration closing next week for the District of Columbia's summer youth jobs program, the city so far has 20,846 teen-aged job applicants and estimates it can provide about 16,100 jobs with the government or nonprofit groups this year.

This compares with about 18,000 summer jobs in the public and nonprofit sectors that the District sponsored last year with its own and federal funds, and includes about 600 added under the recently enacted federal emergency jobs bill.

The Greater Washington Board of Trade, meanwhile, launched its own 1983 summer jobs campaign for the region yesterday, hoping to rely on a combination of Redskins fever and tax breaks to get area businesses to provide more private-sector jobs at a time when government resources are diminishing.

Board of Trade President Thomas J. Owen, chairman of Perpetual American Savings and Loan, acknowledged that this will not be an easy task this year because of the continuing recession.

"Business is still not back to par," Owen told a news conference to kick off this year's campaign. "I've got to use a wet noodle to whip business into hiring youth this summer."

Last summer, private businesses in the Washington area gave teen-agers a total of about 12,000 jobs. Most involved businesses hiring students directly, with about 2,000 going through the Board of Trade's summer jobs referral program, the board estimates.

The board started early this year in trying to get businesses involved in its program, and so far has a commitment for 1,200 jobs in the area. About 75 percent, or 900, of these are in the District and will go to D.C. youths, a spokesperson said.

Overall unemployment in the District in January was 10.4 percent, but youth unemployment is much higher.

In 1982, according to the latest city government figures available, youth unemployment in the city averaged 36.9 percent.

At the board's campaign kickoff yesterday, Frances Graham, director of the D.C. summer jobs program, said there will be more jobs this year in word-processing and in graphics than in the past--part of an effort to put young people into jobs where they will be trained for employment in growing fields.

More than half of the city's 16,100 summer jobs are funded by the federal government.

An infusion of $544,000 under the emergency jobs bill added only 600 to the previous total after administrative costs were taken out, Graham said.

The federally funded jobs are targeted for disadvantaged youths, but there is no such restriction on the city-funded jobs, Graham said.

A total of 17,221 available jobs have been identified, so the city can be selective in picking the most appropriate ones, she said.

Some of the identified jobs are for computer aides and word-processor workers at the U.S. Treasury Department, the D.C. National Guard, the Peace Corps and the Capital East Drug Abuse Program, according to the D.C. Department of Employment Services. Other jobs are for theater employes, messengers, file clerks, parking attendents, police aides and security guards, photographers, plumbing assistants, printing shop helpers, child care aides, counselors and recreation aides.

The Board of Trade's campaign slogan is "Let's Get All of America Working Again," and Redskin Coach Joe Gibbs is featured in TV and radio ads "urging business to make youth a part of your team."

The board also is stressing that a federal jobs-tax credit is available to employers who hire "disadvantaged" youths.

This credit can equal up to 85 percent of the first $3,000 in wages, so businesses "can put young people to work for the price of a cup of coffee per hour," a board official said.

Former Redskin Larry Brown, chairman of the board's summer jobs campaign, and Redskins quarterback Joe Theismann launched the effort yesterday at the board's downtown offices.

"The only way we are going to keep the kids off the street . . . is to give them a job," Theismann said.