ROME, NOV. 17 -- Moving quickly to try to avoid a protracted political crisis, President Francesco Cossiga asked outgoing Prime Minister Giovanni Goria today to put together a new coalition government.

After meeting with the president for 30 minutes, Goria, who resigned Saturday after 109 days as head of the nation's 46th postwar government, agreed to try to rebuild the same five-party coalition that collapsed last week because of disagreements over the country's 1988 budget.

"I think the prospects are good," said Goria, at 44 the youngest Italian to be prime minister. "Let's hope we can find the right conditions."

Such conditions would be an agreement to bring the small Liberal Party back into the coalition. The Liberals brought about the collapse of Goria's first government by pulling out of the coalition in a budget dispute. They charged that a revised 1988 budget proposal failed to cut spending and reduce taxes, as they had demanded.

The Liberals won only 2.1 percent of the vote in last June's parliamentary elections and have only 11 representatives in the 630-seat Chamber of Deputies.

But they have been part of the five-party coalitions with the dominant Christian Democrats and the smaller Socialists, Social Democrats and Republicans that have ruled the country almost exclusively since 1981.

Goria could form a government with a comfortable majority without the Liberals. But because they held the important defense portfolio in Goria's previous government, there is concern among political leaders that if the Liberals were left out of the next government, there could be a battle over which of the other parties should be alloted the Defense Ministry.

Goria today closeted himself with the leadership of his Christian Democratic party, then met with Liberal party leader Renato Altissimo.

Altissimo said he defected from the government last week because it went back on a previous agreement to cut spending and lower taxes. The initial budget proposal would have kept government borrowing at roughly $89 billion, the same level as this year. The revised budget sought to trim that down to $84 billion by dropping the tax cut proposals favored by the Liberals instead of slashing government spending.

After meeting with Goria for more than an hour and half tonight, Altissimo said he remained "hopeful" that a solution could be worked out.