Italian Prime Minister-designate Amintore Fanfani today officially told President Sandro Pertini that he had succeeded in forming a new, four-party coalition government, although tough interparty bargaining over Cabinet posts continued.

Headed by the 74-year-old Fanfani, the new government, the 43rd since World War II, marks the return of the dominant Christian Democrats to the premiership after an unprecedented absence of nearly a year and a half.

Expected to take office next week, the Fanfani Cabinet will replace the five-party government headed by Prime Minister Giovanni Spadolini that resigned two weeks ago because of political and economic divisions, particularly between the Christian Democrats and the Socialists.

The complex negotiations that led to formation of the new government indicate that those divisions remain. But it is hoped that Fanfani, a four-time prime minister and head of one of the most powerful factions of the Christian Democratic Party, will have more clout to deal with them than Spadolini. The latter's Republican Party, though highly influential, controls a meager 3 percent of the popular vote.

The new coalition of Christian Democrats, Socialists, Social Democrats and the tiny, right-of-center Liberals reached final agreement Saturday on a detailed, 28-point austerity package designed to deal with Italy's growing economic problems.

Yesterday, however, the Republicans decided to boycott the new government. Strongly committed to economic discipline, Spadolini and his colleagues were angered by last-minute compromises on key economic issues Fanfani agreed to in order to assure Socialist and Social Democratic approval.

Italy's unions and pensioners had reacted sharply to parts of the strong program designed to bring an inflation rate of more than 17 percent down to 13 percent next year and 10 percent in 1984.

The program calls for a strict ceiling on real wages in the next two years and for sharp cuts -- of at least 15,000 billion lire, or $10 billion -- in a highly inflationary, runaway public deficit that could soon near 100,000 billion lire (about $70 billion), or 15 percent of gross domestic product.

To gain the approval of the left-wing parties, Fanfani had to eliminate pledges to keep pension increases to the 13 percent inflation limit, to reduce public-health spending and to take firm executive action if unions and management failed to agree on a replacement for the wage indexing system that expires Jan. 31.

Union opposition has been only somewhat mollified, and the new government will also have to deal with vigorous opposition from the powerful communists, who last week called for a "democratic alternative," or left-wing alliance, instead of the old policy of "historic compromise" with the Christian Democrats.