Congress' controversial budget process should be retained but strengthened to include more effective enforcement tools, a blue-chip organization of business and academic leaders urged in a report issued yesterday.

The Council for Economic Development, composed largely of corporate executives and university presidents, also suggested a new experiment with a two-year cycle for spending bills that, if successful, could lead to biennial budgeting.

In addition, the council proposed automatic stopgap funding for the government so the bureaucracy is not held hostage during periodic spats between Congress and the White House over continuing resolutions. But it urged relatively low spending levels, with no new programs, to encourage passage of regular appropriations bills.

Release of the report came less than a week after Congress ended its long hassle over next year's budget by approving a plan that President Reagan opposed and threatened to ignore.

Rather than radically overhauling the process or supplanting it with a constititional amendment to require a balanced budget, as some have suggested, the council proposed modifications.

It urged that the first budget resolution, which now sets tax and spending targets, be made binding, with ceilings for each category of spending rather than aggregate spending limits.

The council opposed the idea of a separate budget for construction and other capital investment projects and urged Congress to reverse its earlier decision, in the Social Security bail-out bill, to exclude Social Security from the unified budget by 1993. It urged tighter budgetary control over loan and credit programs.

It endorsed continued use of "reconciliation," by which congressional committees are ordered to change existing tax and spending programs to meet budget targets, but urged Congress to focus primarily on entitlement programs and to avoid "extraneous" provisions.