Deputy Secretary of State Kenneth W. Dam said yesterday that the United States sees "circumstantial evidence" of "rather deep Iranian involvement" in the bomb attack against U.S. Marines in Beirut.

He added that "we certainly believe the Syrians must have been cognizant of what was going on."

It was the strongest public statement so far by a senior administration official alleging Iranian and Syrian links to the Oct. 23 attack with its devastating death toll.

Other U.S. officials have made such charges privately or, if speaking publicly, have been less specific than Dam. Dam also kept alive the idea fostered by President Reagan and other officials that the United States plans retaliatory action.

He, too, was deliberately vague, in saying: "Retaliation comes in many shapes and sizes, and we're looking at all of the options."

His comment hinted that debate was continuing within the administration about how it could document its suspicions, what forms of retaliation are practical and what their effects are likely to be on U.S. efforts to resolve Lebanon's civil strife and on U.S. relations with the Arab world.

Dam spoke on "Face the Nation" (CBS, WDVM) after Israeli Defense Minister Moshe Arens charged on the same program that "there is little doubt at all" that Syria was behind the attack.

Dam, asked for his comments, replied: "Well, we're looking very carefully at the evidence and trying to get more specific evidence than the kind of general circumstantial evidence that Mr. Arens was talking about. We see evidence, circumstantial still, of rather deep Iranian involvement, and we certainly believe that the Syrians must have been cognizant of what was going on."

U.S. officials said privately last week that the bombing was the work of a militant, pro-Iranian Shiite Moslem group known both as Islamic Amal and the Party of God, a breakaway group from the main Shiite Amal, with headquarters in a Syrian-controlled part of Lebanon. The breakaway group's Lebanese leader, Hussein Mussawi, has praised the attacks against U.S. and French forces but denied responsibility.

Secretary of State George P. Shultz is known to have raised the U.S. desire for retaliation at a Paris meeting last Thursday with foreign ministers of France, Italy and Britain.

The European governments are understood to have expressed reservations about military actions.

Nevertheless, U.S. officials have kept alive talk of retaliation, as a way of deterring attacks and assuaging American outrage.

Discussions within the administration reportedly have ranged from asking Lebanese President Amin Gemayel to close the Iranian Embassy in Beirut to mounting a paramilitary attack, presumably by non-American forces, against Mussawi's group. However, some U.S. officials are known to have argued that a military strike, even if feasible, could be counterproductive.

Specifically, they argue, it could jeopardize cooperation with Europeans in the multinational force, incite a Moslem reaction that would hinder U.S. efforts to appear impartial in the Middle East and increase the chance of direct confrontation with Syria, whose cooperation is required for resolution of the Lebanon crisis.

Although Arens refused to discuss the subject yesterday, Lawrence S. Eagleburger, undersecretary of state for political affairs, will go to Israel Tuesday for a visit expected to include exploration of greater U.S.-Israeli cooperation to counter Syria in Lebanon.

Shultz reportedly has advocated that the administration abandon the arm's-length posture it has taken toward Israeli forces in Lebanon.

However, at a National Security Council meeting Oct. 18, Defense Secretary Caspar W. Weinberger reportedly argued that increased U.S. cooperation or aid to Israel would harm relations with Arab countries, and administration sources said the dispute remained unresolved.