Prime Minister Adolfo Suarez began working on forming a new centrist coalition Cabinet today after winning effective control of Spain's first freely-elected Parliament in 41 years.

Parties occupying extreme positions were rejected by an electroate clearly wary of re-igniting the ideological conflicts that surfaced in the last free elections here in 1936, leading to civil war and military rule under the late Generalissimo Francisco Franco.

With returns from Wednesday's balloting 90 per cent complete in all areas except Madrid and Barcelona, Suarez' Democratic Center coalition was the projected winner of 170 seats in the Parliament's Chamber of Deputies, only six short of an absolute majority.

The incomplete results also showed the government-backed coalition capturing 105 to 207 elected seats in the Senate. Most of the 41 senators named to the upper house Wednesday by King Juan Carlos also are Suarez loyalists.STSpain emerged from the balloting with two large party groupings occupying the center ground. Challenging Suarez' center-right coalition was the Socialist Party, which expects to have 115 seats in the Chamber when the final results are in.

The balloting pushed Franco's political legacy even deeper into history. Right-winging politicians who sought to run as his political heirs under the popular alliance banner of Manuel Fraga were held to about 8 per cent of the vote and 15 seats in the Chamber. Parties even further to the right, such as the neo-fascist New Force and the Falange, failed to win any seats.

And Franco's most hated enemies, the Spanish Communists, reaped only 7 per cent of the popular vote, which translated into 20 seats in the Chamber because of its distribution.

The Communists, legalized only two months ago by Suarez, ran a restrained campaign, and party leader Santiago Carrillo praised Suarez today for having permitted a fair election.

Strong lefist showings in late-arriving vote totals in Madrid, Barcelona and the Basque provinces of northern Spain cut Suarez' popular vote total down to about 36 per cent. It had soared to 45 per cent in early counting dominated by returns from the rural areas where the Democratic Center built up overwhelming margins.

The socialists, led by 35-year-old Felipe Gonzalez, were attracting about 26 per cent of the popular vote.

Leaders of various parties winning four-year terms in the Chamber included Suarez, Gonzalez, Carrillo and "La Pasionaria" who was elected from the same district in Asturias that she represented in the 1936 Parliament. Gil Robles, Republican war minister in the Civil War, failed to win on the Christian Democrat Federation ticket.

Carios Arias, the last prime minister under Franco, and Blas Pinar, leader of the New Force, both lost their bids for Senate seats.

The smaller parties were severely handicapped by the weighted proportional representation system used to divide up Chamber seats. The two big groups got a 20 to 25 per cent bonus in seats beyond what their popular vote would have brought them in a simple proportional system.

The weighted system was one of a number of advantages Suarez enjoyed in an election that did not represent any direct risk to the powers held by him and by the King, who appointed Suarez last July for a five-year term.

The bonus leaves Suarez and Juan Carlos in a commanding position in dealing with the Parliament and getting it to produce a new constitution to replace the dictorial laws set down during Franco's rule.

Sources close to Suarez said today that he had already begun thinking about assembling a new Cabinet, which will be the third major shuffle since the King came to power on Franco's death 19 months ago.

Suarez did not make any public appearances or statements today because he did not want to appear to be "crowing" about his victory, these sources said.

They predicted that he would not form a Cabinet entirely of Democratic Center politicians. Sure of being able to attract enough minor-party deputies to his coalition to form a majority, he will try to involve small parties in a center-left government of "national consensus," which will try to negotiate a "social pact" of emergency measures to bolster Spain's stumbling economy.

Juan Carlos signaled the intention to form a new Cabinet by naming five members of the current government, including Interior Minister Rodolfo Martin Villa and Foreign Minister Marcelino Oreja, to the Senate.

Beyond these immediate concerns, the results of the orderly election also pointed to longer-term prospects, including:

The continuing regional problems of Spain. The poor southern region of Andalusia gave strong backing to Socialists and Comunists, while nationalist parties in Catalonia and the Basque country won at least 20 seats in the Chamber of Deputies on platforms demanding increased regional autonomy.

These results underlined the continuing explosiveness of the regional problem, at the heart of much of Spain's urban terrorism and one of the main triggers for the Civil War.

Suarez has moved closer to the kind of political legitimacy Juan Carlos is seeking for his government in his campaign to win greater acceptance and aid from Western Europe and the United States. Suarez ia an elected member of Parliament now, and would undoubtedly be chosen as prime minister if a traditional parliamentary system were in use here.

But his refusal to resign from his appointed position and stake it on the election results prevents him from obtaining complete legitimacy in this election.

Felipe Gonzalez is strong enough to determine now what kind of opposition will be offered to the monarch and Suarez as they continue a process that is essentially one of unilaterally handing down democratic reforms that have not yet led to a grass-roots democracy, but have moved Spain far from the days of Franco.