ROME, JULY 13 -- In a move that took Italian politicians by surprise tonight, President Francesco Cossiga asked Finance Minister Giovanni Goria, 43, a Christian Democrat, to try to put together Italy's 47th postwar government. He is the youngest person ever asked to form a government in Italy.

Cossiga's choice of Goria came after the president concluded that Christian Democratic Party leader Ciriaco de Mita, who had openly sought the job, would be unable to form a government because of the bitter opposition of Socialist leader and former prime minister Bettino Craxi.

Goria, who has been finance minister since December 1982, is one of Italy's youngest Cabinet members. The post of prime minister usually is reserved for a party veteran.

Goria was on a visit to Emilia in central Italy when Cossiga told him that he was being tapped to try to bring Italy out of its 4 1/2-month political impasse. He returned to Rome immediately, and after seeing the president said he had accepted the call.

Analysts here were uncertain about his chances of success, but agreed that because he is not one of his party's traditional leaders, any government he forms will not last long.

What he has going for him, analysts said, is the need for some sort of government to take Italy through the summer and into the fall, when next year's budget must be approved by parliament.

The country has been rudderless since Craxi resigned as prime minister in March because of a dispute with de Mita over who should lead the five-party coalition that had given the country a rare period of nearly four years of political stability.

De Mita's insistence that a Christian Democrat, preferably he, should head the coalition, brought Italian politics to an impasse that eventually led Cossiga to dissove the parliament and hold new elections in June.

The elections did nothing to alter the basic balance of power in Italy, though both the Socialists and, to a lesser extent, the Christian Democrats, increased their vote at the expense of the Communists, still Italy's second largest party after the Christian Democrats.

No sooner had the votes been tabulated than both Craxi and de Mita declared the elections a victory for their parties and renewed their feud.

Last week, as Italy's fractious political parties prepared for the ritual consultations with the president about forming a a workable government, de Mita persuaded the Christian Democratic leadership that he should be the party's only candidate for prime minister.

That stand angered even some senior Christian Democratic leaders, and Craxi dealt it a heavy blow when he said that because the current crisis resulted from a dispute between him and de Mita, neither should be considered.

Goria's challenge is to see whether he can put back together the coalition of Christian Democrats, Socialists, Social Democrats, Liberals and Republicans.