McGeorge Bundy warned yesterday that the "existing system of government in the United States, already dangerously weak, needs a double dose of reinforcement--to meet both its present and future responsibilities."

He was delivering this year's second Godkin Lecture.

Recognizing the present weakness at all levels of government--state and local as well as legislative and judiciary, Bundy concentrated on inadequacies in the Federal Executive.

"The simplest demonstration of weakness in the Executive Branch," Bundy said, "is its subordination to Congress in matters of appropriation and taxation." He cited the present impasse over the tax increase as a case of Congress frustrating the Executive.

The Executive Branch is further handicapped, Bundy went on, by the lack of genuine harmony between the President and his bureacracy. This makes it difficult, he said, for there ever to be "sustained, coordinated and energetic" Executive action.

Bundy said that Cabinet officers "should run their part of the government for the Administration--not run to the Administration for the interests of their part of government."

Two other weakness of the Executive Branch, Bundy added, are "under-representation of the public interest" and lack of interconnection between parties legitimately involved.

He illustrated under-representation by the dismal failure of the Federal Communications Commission to regulate the mass media effectively. The lack of interconnection or any mutual understanding between specialists emerges most clearly, Bundy said, in the attempt to formulate a nuclear weapons policy on the advice of both military men and scientists.

Bundy ended by affirming his faith in the office of the President as the "right source of new executive strength" and as the best upholder of the public interest.

The last Godkin Lecture tomorrow will be devoted to the role of the citizen in the modern governing process.