Leaders of West Germany's Christian Democratic and Free Democratic parties said today they would move rapidly next week to conclude negotiations on a new center-right coalition, and aides said privately a parliamentary motion to oust Chancellor Helmut Schmidt's minority govenment could come as early as Wednesday.

Following the breakup yesterday of Bonn's left-center coalition, Christian Democratic leader Helmut Kohl said today at a rally in the state of Hesse that difficult domestic and international conditions made it urgent that a new government be formed.

Free Democratic Party leader Hans-Dietrich Genscher, campaigning in Bavaria, backed this view and said that after a new government is installed, elections should be put off until "the first quarter of 1983" to allow the new government time to institute measures to revive the economy and lower West Germany's unemployment rate, now at a 30-year high.

But still determined to fight to the finish, Schmidt's Social Democrats launched a nationwide drive in support of the chancellor's plea to opponents to refrain from forming a new government and schedule early elections first.

The weekend maneuvering kept political tensions high. It underscored the point that while the way to a conservative-led government was opened by the resignation yesterday of the four Free Democratic ministers, getting there could yet provide this nation with a suspenseful ride. Schmidt's Social Democrats had ruled in a coalition with the Free Democrats since 1969.

Kohl, who heads an alliance of Christian Democrats and their Bavarian counterparts in the Christian Social Union, and Free Democrat Genscher are scheduled to meet Monday for talks on assigning Cabinet positions in a prospective coalition.

The West German constitution, which makes unseating a chancellor in midterm difficult, forces the opposition parties to reach agreement on a new chancellor before challenging the incumbent.

If a deal is struck, the Christian Democrats and Free Democrats plan to seek what is called a constructive vote of no confidence against Schmidt, at the same time putting forward Kohl, 52, to be the new chancellor.

This approach has been tried only once before in West Germany--in 1972 when the Christian Democrats tried to remove Schmidt's predecessor, Willy Brandt, and failed, suffering great embarrassment.

To succeed this time, Genscher must be sure he has at least 23 of his 52 parliamentary deputies in support of aligning with the two conservative parties. This assumes that all 226 deputies in the Christian Democratic Party and the Christian Social Union, will not object to the terms worked out for an alliance with the Free Democrats.

Genscher appeared to have the necessary support yesterday when a vote taken in the Free Democrats' parliamentary group showed 33 in favor of entering coalition talks with the conservatives.

But a later vote in the party's national executive committee, which supported Genscher by a vote of only 18-15, suggested that the split in Free Democrats' ranks may be wider than the parliamentary vote made it appear.

Left-wing Free Democrats, opposed to a break with the Social Democrats to start with, worry that lining up with the conservatives would damage the Free Democrats' credibility. They also object out of principle to the formation of a new coalition in closed-door negotiations before the prospect of a center-right alliance can be considered at the Free Democrats' national party congress in Berlin, scheduled to begin Nov. 5.

Indicating the seriousness of the divisions, the party's general secretary, Guenther Verheugen, said today he would resign as a result of the break with the Social Democrats, which he had opposed.

Genscher, the former foreign minister, enters the talks with Kohl from a weak position. In addition to the splits in the party, the Free Democrats have slid severely in national polling since they scored 10.6 percent running alongside the Social Democrats in 1980 elections. In Hamburg elections in June, the Free Democrats failed to clear even the 5 percent required for representation.

Nevertheless, for Kohl and other Christian Democratic moderates an alliance with the Free Democrats is attractive because it affords a political balance to Franz Josef Strauss, the leader of the Christian Social Union and an overpowering right-wing figure, who might otherwise tend to dominate a new conservative government.

Further, a number of conservatives make the case that by founding a center-right coalition now rather than trying to form a one-party government after an election, their chances of staying in power longer would be better, given modern German history. Polls suggest that in an election, the two conservative parties could win enough seats in parliament to rule as a majority government.

One potential stumbling block in next week's talks is a decision on the timing of elections. Genscher prefers sometime around next March, but Strauss made it plain today that he wants them immediately after the Social Democrats are ousted, believing the conservatives can win an absolute majority. It is not clear what date Kohl prefers.

The Social Democrats are in the meantime showing a sort of sunset brilliance in their final days. Schmidt's address to parliament yesterday was applauded by even the conservative West German press today as a cool, dignified performance. Looking forward to regaining some of their ideological and political force in the years ahead as an opposition party, a number of Social Democratic deputies hope to use new elections to demonstrate the party can at least exist with some flair.

Gone, or at least submerged now, are the tensions that for years kept Schmidt, in West German terms a conservative in many respects, at some distance from his left-leaning party. Acknowledging a renewed closeness, the Bonn leader gained one of his most vigorous bursts of applause from Social Democratic deputies yesterday when he declared that "complete trust exists between the chancellor and the Social Democratic Party."

For Schmidt and his party, the villain is now clearly Genscher. "Schmidt has been reunited with his party," an aide to the chancellor observed this week. "But the price he has had to pay for this has been the end of his government."