The District of Columbia is spending about $15 million a year to lease space without knowing how much space it owns or needs, the General Accounting Office said in a report released yesterday.

"Without an improved system and adequate information, the District cannot know how many square feet of space it needs," the GAO report said.

The GAO, which conducts studies and audits for Congress, noted that the city is now devising a new space-reporting system and conducting a citywide building survey that should correct the problem, but recommends that until that is done, the city should not buy any new properties.

Harold Henson, the city's chief contracting officer, disagreed with the report, contending that the GAO had presented no evidence that the city is uninformed about space use.

Henson said yesterday that the city knows how much space it has and needs and is not leasing space or seeking to buy new buildings unnecessarily.

Henson criticized GAO's methods of conducting the study, asserting that it was compiled after talking to unnamed officials and reviewing a few reports and documents.

The report, signed by GAO director William J. Anderson, said the agency had reviewed all 24 leases that the city had signed or renewed in fiscal 1981, and had interviewed employes familiar with the leasing process.

The GAO said it found that Henson's Department of General Services, in all 24 leases, had failed to validate the amount of space requested by city agencies or reconcile that to the number of employes who would use the space.

The report said that a 1979 oversight report found that District government storage areas were only 61 percent used, and that department officials could not supply current comparable figures for space use in D.C. warehouses.

Henson, in a letter to GAO last Jan. 19, said the city leases 1,378,600 square feet of space at an annual cost of $11,009,640, and that the city expects an annual increase of about $1.5 million to rent the same space during the next three to five years.