Washington — In the wake of the Grenada invasion, the Reagan administration is stepping up efforts to counter the diplomatic fallout throughout Western Europe. Administration officials say that opinion in Europe is shifting as America states its case for the intervention. But these officials are still concerned about the magnitude of unfavorable reaction in West Germany, Britain, and other NATO countries.
A high-level US official may soon be sent to European capitals to explain the American rationale for the invasion and United States intentions regarding the Caribbean island, according to State Department officials. Since the Grenada action, they say, the US has sent a steady stream of messages and briefing papers to its embassies in Europe and elsewhere in order to inform foreign governments. Presidential communications have also been sent to British Prime Minister Margaret Thatcher and other leaders through their embassies here.
''The reactions in Europe are not a source of overwhelming anxiety,'' commented one US official, ''but they are not something we want to see continuing or creating difficulties in other areas. So we will make an effort to explain our position.''
West Europeans are worried about the impact of the Grenada action on the coming deployment of US nuclear missiles.
So far, the governments have weathered public opposition to the pending deployments. But the US move into Grenada has given the Soviet Union a ''field day'' in its vigorous propaganda effort to thwart installation of the missiles, say officials here. The European antinuclear peace movement, they say, feels it has a new lease on life.
European diplomats here do not see the transatlantic row as dangerous, but they express unease at how the US has handled the issue. ''It's not only the matter of a lack of consultation,'' said one, ''but of the fact that the evidence and justification for the Reagan policy has been coming out in dribs and drabs.''
Much of the European concern will dissipate, diplomatic observers say, if the US quickly gets its troops out of Grenada, replaces them with a multinational peacekeeping force, and sets in motion the process of establishing a democratically elected government there.
The administration, in fact, seems to be moving rapidly in this direction. The Defense Department has announced that hostilities have ended in Grenada and that American troops will begin leaving the island soon. How many of the 5,000 troops will stay behind has not been made clear.
According to diplomats here, the European concern is that all the Western democracies have been tarred by the American invasion, making it harder for them to argue against Soviet actions around the world. But the view of US administration officials is that, whatever European leaders say publicly for domestic consumption, the strong American action will in the end be seen as demonstrating US resolve to stand up to Moscow - and therefore as a firm commitment to the defense of Europe.
The deployment of US medium-range nuclear missiles in Europe, American officials note, comes in response to European fears that the US might not be willing to employ its nuclear forces in the event of a Soviet attack.
''In the short term, the Grenada action is inconvenient for the Europeans and puts pressures on them,'' said one US official. ''But the fact that the US is prepared to take risks to protect its people and interests can only heighten their confidence in the credibility of the US security guarantee, which has been undermined by US vacillation in the past.''
White House officials say they believe that as more facts come out about the Grenada situation they will win European support for the invasion. It is being pointed out, for instance, that the initial call for help came from the British governor-general of the island.