The Arms Control and Disarmament Agency yesterday responded almost instantly to a State Department spokesman's suggestion, published in yesterday's Washington Post, that State, not the agency, has the leading role in coordinating arms control policy.

Jim Pope, acting public affairs adviser at the ACDA, called The Post yesterday morning on instructions from his superiors to insist that his agency would play the leading role, as the law establishing it said it should.

Noting the State Department spokesman's contention that State "has and will continue to take the lead in this administration, coordinating policy required to prepare for and support the conduct of arms control negotiations," Pope said:

"This statement was not cleared with ACDA, and it is factually inaccurate. The 1961 arms control and disarmament act gives this agency responsibility for preparing and managing U.S. participation in international arms control and disarmament negotiations. This function is exercised under the direction of the president and the secretary of state. Mr. Rostow Eugene V. Rostow, the new ACDA director in his confirmation hearings made clear that he would fulfill his responsibilities in preparing for arms control negotiations in accordance with that statute."

Rostow assumed office at the end of June, and Pope noted that, in the first six months of the Reagan administration, State Department officials tried to assume some of the responsibilities that fall within ACDA's purview.

Richard Burt, the State Department's director of political-military affairs, has been acting as chairman of the interagency group preparing arms control policy.

Pope said the department spokesman's statement indicated that there was a "battle" going on about which the ACDA had been unaware.

"I don't know what they're trying to do," the ACDA spokesman said of State.