Mayor Walter E. Washington asked a Senate subcommittee yesterday to abandon a proposal that would put stricter restraints on the CETA program in the District of Columbia than in other cities around the nation.

The mayor urged Sen. Patrick J. Leahy (D- Vt.), chairman of the Senate D.C. appropriations subcommittee, to wait and see what new guidelines are placed on the Comprehensive Employment and Training Act by congressional committees that oversee the program nationally.

Leahy's subcommittee is scheduled to meet today to act on the city's proposed 1979 budget of $1.3 billion. On Monday, Leahy proposed several restrictions on the city government's use of CETA - paid workers that he suggested be written into the budget bill.

His proposals responded to a Labor Department report last month that found abuses in hiring and assignment of CETA workers on the City Council staff.

Council Chairman Sterling Tucker, in a letter sent Tuesday, and Mayor Washington, in a letter sent late yesterday, both called upon Leahy to drop his proposed restrictions.

Tucker said the council will meet in a special session Monday to adopt strong guidelines on hiring and staff assignments and "to guard against political activity or the appearance of political activity" by CETA workers.

He also noted that other committees of Congress are dealing with nationwide rules for the assignment and pay of CETA workers.

"Your proposals," the mayor wrote Leahy, "are more restrictive than some that are pending (elsewhere) in Congress. Thus, your proposals have the potential of creating inequities in treatment of employes in the (D.C.) program and imposing a punitive condition that may not be imposed on other employes in cities throughout the nation."

Leahy has proposed limiting all CETA employes to $15,000 annual pay, which would directly affect nine of the 60 CETA-paid council employes paid above that amount. Leahy also would limit employment under CETA to 24 months and prohibit assignment to council committee staffs.