Health and Human Services Secretary Margaret M. Heckler yesterday ordered a hiring freeze on all 5,700 slots in the office of the secretary as the first step in a plan to streamline department operations.

In addition, department sources said a special task force headed by Heckler's chief of staff, George Siguler, is recommending that the number of jobs in that division be cut by between 1,000 and 1,200 over the next two years.

Between 500 and 600 jobs would be eliminated permanently, through attrition wherever possible, according to department sources.

The remaining half of the cut would be achieved by shifting slots out of the office of the secretary to other divisions of the department.

Overall, the department has about 142,000 full-time-equivalent jobs.

One department official said the changes "do not involve cuts in services" or benefits to the elderly, sick and poor, but merely an effort to simplify and reduce the department's overhead.

In addition to the secretary's immediate staff, the office of the secretary includes the inspector general and his staff, the office for civil rights, office of consumer affairs, office of the general counsel and the offices of five assistant secretaries, for legislation, management and budget, personnel administration, planning and evaluation and public affairs.

In a memorandum to office heads, Heckler said the hiring freeze, which will not apply to those who already have "firm written offers of employment" or who possess skills not otherwise available, is intended as the first step in carrying out the general objectives of the President's Private Sector Survey on Cost Control. The survey, a group of businessmen headed by J. Peter Grace, reviewed the executive branch for President Reagan, suggesting budget cuts and efficiencies.

However, the 1,200-job reduction is several hundred less than recommended by the Grace group.

In addition, sources said, the Siguler task force rejected one of the key concepts advanced by the Grace Commission, namely, extreme decentralization of the department.

That would have left the secretary as a sort of chairman of the board with little operating staff for real decision-making and leverage, the sources said.

Instead, they said, the Siguler group decided to recommend cutting or shifting duplicative positions and slots that are simply servicing the operating divisions rather than helping the secretary directly.