This week in Moscow is as important as last week in Washington in determining the results of the Reagan-Gromyko exchange. How President Reagan came across to the Soviet foreign minister - as genuinely interested in negotiations or preoccupied with an American arms buildup; as detached from the foreign policy process, and thus a creature of his aides, or informed and in control of foreign relations; as capable of perceiving pragmatic Soviet intentions or viewing the Kremlin through an ideological haze - all this will be reported back to the Politburo. The Soviet leadership itself is in transition: The Gromyko report could influence the makeup of the Soviet command as well as the context for superpower relations.
The administration worked hard to give the impression that the Soviets could do business with a Reagan Washington. It did its homework. It promoted the useful idea of trying to get multiple levels of communication going between the superpower capitals. For the near term, some kind of progress could soon surface in two areas: in space treaty talks, or a reopening of the intermediate nuclear missile talks. A third outside area could involve the Middle East, possibly in the Persian Gulf or some change in Soviet attitudes toward Israel.
The State Department also had a political goal in mind, quite apart from the obvious US election outcome. Secretary of State George Shultz needs to set some kind of constructive US-Soviet agenda for a second Reagan term. To begin a second term without a positive tone and direction for US-Soviet relations, coming out of a compaign that many may construe as a powerful mandate for the incumbent, could prove a serious and dangerous handicap. A battle royal for the direction of the Republican Party is anticipated, whatever the outcome in November. Already GOP ideologues are deriding Mr. Reagan's new conciliatory tone toward the Soviets as ''son of detente'' and ''Detente II.''
The President, if reelected, would still have to deal with the split in his own ranks over doing business with the Kremlin. His is not the first administration where the Pentagon has opposed State Department and White House initiatives for accords. President Ford acknowledges now that, in putting Donald Rumsfeld in the Defense Department, he failed to pressure the Pentagon hard enough on its resistance to SALT II. Presidents Nixon and Carter had a different experience; their defense chiefs, Melvin Laird and Harold Brown, were supportive of arms control efforts; notably, agreements were struck in these administrations.
The American political judgment on the Reagan-Gromyko parley will follow its own course, apart from its impression on the Kremlin. Was the bid to talk an 11 th-hour conversion on Mr. Reagan's part? Did Mr. Reagan look uncharacteristically uncomfortable in the Soviet minister's presence? Was their eight-minute private dialogue, observed unheard through the Oval Office window, in which they gesticulated vigorously, a show of resoluteness for the cameras outside? Or was this the moment some deal was struck? At the least, Mr. Reagan was acting in accord with the majority American public view that his administration should be on talking terms with their Soviet counterparts.
The ''trust'' factor plays as strongly from Moscow's point of view as from Washington's. The Kremlin has cast the Gromyko-Reagan talks in the worst possible historical framework, its dealings with Hitler's Germany of the 1930s. This might have been a ploy for concessions, or a defense against an unsuccessful outcome.
But it is a fact that Ronald Reagan has a barrier to cross in getting the Soviets to negotiate. They see him as a stimulus for America's new mood of buoyancy and self-confidence, with what they see as a strain of ultranationalist militarism mixed in.
We hope Mr. Gromyko reports back that the Kremlin has good reason to resume constructive talks with the Washington leadership.