THE fall of Turkey's coalition government, led for the last two years by Prime Minister Tansu Ciller, has thrown this pivotal nation into political instability. The collapse of the coalition between center-left and center-right parties surprised most observers here. Many believed the newly elected chairman of the People's Republican Party, Deniz Baykal, was ready to continue the partnership. But after a three-hour meeting between Mr. Baykal and Mrs. Ciller on Wednesday, he announced his party was pulling out. Baykal's party has pushed Ciller to become more aggressive in her pursuits of reforms. She has initiated a set of democratic and economic changes to turn Turkey into a regional power and to boosts its ties with the West, which criticizes Turkey's human rights record. Conservative members of government have dragged their feet on the reforms, fearing an ethnic Kurd rebellion and a rising Islamic movement. Baykal has insisted on a firmer commitment to democratic reforms, especially the repeal of an antiterrorism law that allows easy detention of dissidents. And he is calling for pay raises for public workers and stricter controls on Islamists he believes are a threat to Turkey's secular-run government. He also wants the removal of the chief of police in Istanbul, Necdet Menzir, for his statement attacking the government's minister in charge of human rights.. Forming new government In the near future, Ciller, Turkey's first woman premier, could make a comeback as head of a new coalition government. Or, if she fails, a caretaker government could carry Turkey to early elections, possibly by the end of this year. President Suleyman Demirel, who has not supported many of Ciller's democratic reforms, is consulting with political leaders to decide what course to take. Mr. Demirel may assign the speaker of the house, Husamettin Cindoruk, to form a caretaker coalition Cabinet that could include Ciller's True Path Party and Mesut Yilmaz's Motherland Party - both center-right groups commanding a solid majority in Parliament. Together they could lead Turkey to the polls. The house speaker says he is prepared to lay the groundwork for elections next December. Although polls are not usually held in Turkey during winter, because weather conditions prevent many people in the eastern provinces from voting, most political parties represented in Parliament, including the social-democratic People's Republican Party, the Motherland Party, and the pro-Islamic Welfare Party are calling for early elections. Ciller's party wants elections to be held at the scheduled date, which is fall 1996, and to carry on the job of governing with a new coalition partner until then. After presenting her resignation, she said, ''What we need is not a government for elections, but a government for seeking solutions.'' Ciller appears determined to fight to be the head of a new government, taking the Motherland Party as a partner. Insiders say she may agree to advance the elections to next spring - but she opposes any earlier date than that because of her commitments to complete entry to the customs union with the European Union and the oil pipeline project from Azerbaijan to southern Turkey. If she can make the deal with Mr. Yilmaz, leader of the Motherland Party, she will be able to carry on as prime minister until the date of the elections. End of an experiment The fall of Ciller's coalition ends the experiment of a moderate right-and-left partnership in Turkey. But it may open the way for a union of two moderate right-wing parties, whose basic programs are similar. Political analysts say that this could enhance the chances of the moderate right in the next elections and remove the danger to Turkey's secular government of a victory by the pro-Islamic Welfare Party, which has recently become the most popular party. The current political crisis comes at a time when Turkey faces major foreign-policy decisions. The European Parliament will vote on Turkey's customs union on Dec. 14, before which Turkey is expected to take steps for democratic reforms, change its antiterrorism law, and release political prisoners. ''If Turkey does not fill those obligations, the vote will be negative,'' says Michael Lake, the EU's ambassador in Ankara. ''The question now is whether the Turks will be able to take such action, while they are preoccupied with political uncertainties.'' Similar actions are required on other issues, such as the Kurdish rebellion in the southeast and economic programs initiated by Ciller. Ciller has been criticized for handing over responsibility for fighting terrorism to the Army. Last spring, 35,000 troops crossed into northern Iraq to crush the rebellion by separatist Kurds. The Army has been accused of committing many human rights atrocities in its quest. If Turkey wins its bid for an oil pipeline from Azerbaijan to southern Turkey, it would be a huge boost for its faltering economy.