Italy's ruling Christian Democrats offered a compromise plan yesterday for a new Cabinet which, if accepted by the Communists, could give Italy its first government with formal Communist support in three decades.

The Christian Democratic offer, hammered out at an all-day meeting of the party's 40-member Executive Committee, appeared to be a cautious attempt to meet Communist demands for a greater political role by allowing them to give official parliamentary backing to a new government.

The Communists, who have been under pressure from their members to demonstrate the success of a 1 1/2 year policy of close cooperation with the Christian Democrats, may find themselves unable to accept the document and its Byzantine phrasing.

The Christian Democrat statement, which again ruled out Cabinet Posts for Communists, backs into the compromise offer by recognizing that the previous system of abstention, through which the Communists and four other parties gave indirect support to a minority Christian Democratic government, has come to an end.

This may not be enough for the Communists, whose minimum request has been for a "negotiated, recognized and explicit" bid for their support. The offer nevertheless represents an unprecedented step forward in the complex political negotiations between Italy's two major parties.

Its potential for upgrading the Communists' role also indicates that the American government may be disappointed in its expressed hopes for a reduction of Communist influence here.

The plan gives Premier-designate Giulio ndreotti a mandate to try to form a government based on a fourpoint joint program that would be monitored, at regular intervals, by special committee of parliamentary party leaders including Communists. For the first time, it would give the Communists a voice in Italy's foreign policy.

A highly-placed Christian Democrat described the party's move as a major concession to the Communists, whose demands for a greater decision-making role brought down Andreotti's previous government almost three weeks ago. The Communist Party is the second-largest in Italy.

The carefully worded offer also appeared to be a last-ditch attempt by the Christian Democratic leadership to find a solution for this country's political crisis and avoid new national elections without incurring the wrath of those members of their own party who vociferously oppose a political alliance with the Communists.

The new joint program, which would replace a six-party accord worked out in July, would stress the need for finding solutions to Italy's major problems - rising crime and terrorism, economic recession and growing unemployment.

The new Andreotti plan would also extend intra-party cooperation into the field of foreign affairs, a sector over which the Communists have made no influence since the period between June 1945 and May 1947 when they participated in four coalition governments with the Christian Democrats and several other parties.

This gesture implicitly gives credibility to the Communists' increasingly frequent claims of commitment to the West and to NATO.

The influence of the powerful Italian communists increased sharply after the June 1976 elections when their 34 percent of the votes trailed only a few points behind the ruling Christian Democrats.

The Communists, who command considerable support among Italy's workers and low income groups, have given crucial support to Andreotti's minority government since it was formed in August 1976.

The Communists' demands for greater formal recognition have been supported by the Christian Democrats' former allies, the Socialists, Social Democrats and Republicans, who have refused to join any government coalition from which the Communist Party is excluded.

The Christian Democrats, on the other hand, have always been unwilling to give formal recognition to the Communists' influential role.

Inside sources say that top leaders of the Christian Democratic Party may have been further intimidated by the Jan. 12 statement by the U.S. State Department expressing strong opposition to Communist membership in any government here.

According to one top Christian Democrat, "What we've been looking for is a plan that will enable the Communists to claim they are part of the government majority and for us to say they are not."