After several weeks of intense Communist pressure, four of the six parties currently supporting Italy's minority Christian Democratic government have officially asked for a change of government that would give the powerful Communist Party a greater political role here.

A three-hour meeting yesterday between representatives of the six parties that last July signed a joint program ended with a call by Socialists, Republicans and Communists for a revised, broadly based government, and with a request by the small Social Democratic Party for changes that would upgrade the Communist role but fall short of giving them posts in an Italian Cabinet.

A high-ranking Communist said yesterday's development was tantamount to a vote of no-confidence by four of five parties that for the last 17 months have given crucial parliamentary support, through abstention, to Premier Giullo Andreotti's government.

"The Andreotti government is finished," the Communist said, illustrating the sharp turnabout in Communist tactics that has occured here in recent weeks.

From the June 1976 elections until recently, the Communists, Italy's second largest party, were Andreotti's major supporters.

But the situation changed radically in early December. The Communists began calling for Andreotti's replacement and Party leader Enrico Berlinguer went on television to say his party would not settle for anything less than "a government formula that would give Communists, Socialists and Christian Democrats, as well as other parties with a contribution to make, equal importance."

The Communists claim that their shift to a hardline position merely reflects their conviction that the July political program has not been effectively applied and that the country's grave econimic problems require government by a broad national coalition rather than a minority government.

"Our people have got to be up there at the highest levels both to monitor policy and to convince left-wing Italians that the sacrifices called for by the government are really on the level," a Rome Communist said.

But many observers here believe the Communist about-face stems instead from internal party disagreements over strategy at a time when membership in some areas of the country is flagging.

Ever since they began supporting the Andreotti government, Italy's Communist leaders have had trouble explaining to their rank-and-file just why support for their traditional foes, the Christian Democrats, should be seen as a feather in the Communist cap.

Dissatisfaction with the party's conciliatory attitude toward the Christian Democrats has already led many young people to shun the party in favor of far left extremist movements.