Italy's unexpected decision to stay out of the new European Monetary System because of insufficient offers of financial assistance has heated up a debate over the economic pros and cons of the matter and threatened to endanger the stability of Premier Giulio Andreotti's minority government.

The move by the 54-year-old Andreotti, Premier now for over two years, has come under sharp attack from the small but influential Republican Party and from the right wing of his own Christian Democratic Party, which has accused him of pandering to the communists.

On Sunday the powerful communist party, which supports Andreotti in parliament, stepped up its criticism of the European Monetary System and suggested that Italy should put off joining until its own economy becomes stronger.

Faced with a French refusal to use the Common Market regional development fund as a conduit for a vast transfer of resources to poorer community countries like Italy and Ireland, the Italian premier is thought to have preferred to back down on an earlier policy decision rather than risk loss of his essential communist backing.

The week-long "pause for reflection" he announced Tuesday in Brussels is thus likely to be used to drum up support for his "no entry" position when Parliament votes on the subject next Wednesday.

However, the question of adhesion to the new monetary system that was to have linked the currencies of nine countries has been controversial here from the start.

Two of Andreotti's key economic cabinet members, Foreign Trade Minister Rinaldo Ossola and newly-appointed industry minister, economist Renato Prodi were opposed, while the Governor of the Bank of Italy, Paolo Baffi, insisted that joining without Great Britain -- which has also stayed out -- for Italy would be a disaster.

These men and other politicians and economists were and are convinced that even with the special six percent fluctuation margin granted to Italy, 3.75 points higher than the norm, the country would not have been able to keep pace with France, Germany and the other member countries.

At present the lira is much weaker than any other currency in the system. The Italian inflation rate is eleven points higher than that in West Germany and six points higher than the Common Market average.

Adhesion was thus said to mean automatic devaluation with respect to those currencies, and reduction of purchasing power at home, higher production costs and a drop in foreign trade competitivity at a time when the Italian economy is recognized to be highly fragile.

It would also mean giving up exchange rate regulation which over the last ten years has been this country's major instrument for correcting serious economic imbalances. Since Feb. 9, 1973 when Italy abandoned a fixed currency rate, the Lira has declined in value by over 40 percent.

Supporters of membership, which include the Republicans and a broad sector of the Italian business and industrial world, believe instead that only by accepting the stringent monetary regulations of the new system would Italy be forced to conduct the rigorous economic policy it has sorely lacked in the past.

They also maintain that non-membership will mean Italy's exclusion from the great European economic decisions of the near future. Premier Andreotti had accepted these arguments, convinced furthermore that a triumphant entry into the system would have further consolidated his own position here at a time when the likelihood of a government crisis has been growing.

However aware of communist and trade union concerns, from the start Andreotti had linked Italian entry to a substantial transfer of resources that would have enabled Italy to bring its economy into greater harmony with those of its community neighbors.

French President Giscard D'estaing's insistence that Italy's requests for aid, said to amount to more than $2 billion over five years, were "out of proportion" pulled the rug out from under Andreotti's feet, or so at least his opponents here are claiming.

Others, who consider Andreotti a tactical genius, believe the magnitude of his demands may have reflected his realization that joining the monetary system now, before a new three-year anti inflation plan goes into effect, could have had serious political consequences at home.