A House committee approved a bill yesterday to permit unrestricted picketing at most construction sites.

The House Labor and Public Welfare Committee voted 22 to 11 to send the common situs picketing bill to the House floor.

Republicans have strongly oppose the bill, while the AFL-CIO has waged a battle for its enactment. President Carter says he will sign the measure if it reaches his desk.

The legislation would make it legal for a union to picket an entire building site even though its dispute was with only one subcontractor. Currently, a construction union that pickets a nonunion subcontractor is restricted to a separate entrance gate used only by employees of that subcontractor.

The committee amended the bill to exempt small builders.

Builders that have constructed fewer than 20 houses in a previous 12-month period would be exempt, and the exemption also would apply to a location where no more tha five swellings are being constructed.

The committee also narrowed the rights of construction workers to picket construction sites that are adjacent to, or part of, an industrial plant.

For example, construction workers could picket at entrance gates used by construction workers, but could not picket at gates used only by industrial workers.