West Germany's 13-year-old center-left coalition collapsed today when the government's four Free Democratic ministers resigned and Chancellor Helmut Schmidt, minutes later, went before the parliament to urge new national elections as early as possible.

The moves climaxed months of strain between Schmidt's Social Democrats and the small centrist Free Democratic Party over foreign, security and especially economic policy. But they left uncertain the timing and procedures under which a new government -- expected to be led by the conservative Christian Democrats -- would be formed.

Helmut Kohl, the Christian Democratic leader, and Hans-Dietrich Genscher, the Free Democratic leader who today quit his post as foreign minister after eight years, rejected Schmidt's appeal to refrain from trying to set up a new government before new elections could be held around the end of November.

Instead, the two party chiefs declared they would begin negotiations next week on a new coalition that would oust the Social Democrats and delay elections until a time of their own choosing, perhaps next spring. Kohl called on Schmidt to do his "patriotic duty" and resign.

But the West German leader appeared determined to remain in office for the time being as head of a minority government. He named himself to assume the foreign minister's duties and appointed three current Social Democratic Cabinet members to take on the additional assignments of the three other ministries vacated by the Free Democrats -- economic affairs, interior affairs and agriculture.

If the conservatives do assume power, the main changes are expected to come in domestic, not foreign, policy. A more pro-American tone could emerge, but the commitment of the Christian Democrats to detente with the Soviet Union differs little in substance from Schmidt's. In budget policy, West German conservatism is more tempered than that of the Reagan administration or of Margaret Thatcher in Britain.

Triggering the government's long-anticipated breakup was Schmidt's decision, reached last night, to try to force new elections. Explaining his reasons for bringing matters to a head, the 63-year-old chancellor told a crowded parliament chamber that the coalition's tensions in recent days had paralyzed the government.

"In the interest of our country, in the interest of our parliamentary democracy and in the interest of the Social Democratic Party, I cannot and will not continue watching how the capacity for action and the reputation of the federal government is being constantly damaged," Schmidt declared.

Backed by frequent enthusiastic applause from Social Democratic deputies, he lashed out at his former coalition partners for statements and maneuvers that he said had undermined confidence in the government's ability to continue. In an unusual personal assault on Genscher, Schmidt singled him out for beginning a year ago to hint at a split by speaking of a "turn" in German policy and never making clear his intentions about the coalition.

But Genscher, answering Schmidt's charges in his own parliamentary address, blamed the coalition split on the Social Democrats. He said they had cut away the ground for compromise on economic policy by resisting budget cutbacks and demanding higher taxes. He also attacked the Social Democrats for sniping repeatedly at budget compromises that were reached.

"It was not the Free Democrats who questioned any point of these decisions," Genscher said.

Foreign and security policy, too, Genscher said, had recently been dragged into the coalition conflict -- a reference to complaints among left-wing Social Democrats about the ex-foreign minister's public endorsements of plans to deploy new U.S. missiles in West Germany and his generally pro-American tone. He again admonished the Social Democrats -- as he did yesterday in a heated parliamentary debate that finally drove Schmidt to act -- not to deny in their political opponents the will for peace they also have.

Genscher said he had advised Schmidt of his intention to resign, along with that of the other three Free Democratic members of the 16-minister Cabinet, at a brief meeting between the two men this morning.

The Free Democrats had hoped to forestall a final decision on a coalition rupture until after state elections Sept. 26 in Hesse, where they already had abandoned a long-time partnership with the Social Democrats and pledged themselves to a coalition with the Christian Democrats. The conservatives, too, had signaled their intention last week to wait to challenge Schmidt at least until after elections Oct. 10 in Bavaria, where Franz Josef Strauss, head of the Christian Social Union, sister party to the Christian Democrats, is expected to win another mandate as minister-president.

But a rapid worsening of relations in the coalition, brought on this week by the release of a dramatic memorandum written by Economics Minister Otto Lambsdorff, a Free Democrat, washed away slower scenarios for the government's breakup. That memo, which blasted budget compromises up to now for failing to inspire business confidence and proposed drastic welfare spending cuts, caused a sensation among Social Democrats, who viewed it as a provocation to end the coalition.

Schmidt told the parliament that until the middle of the week he had "undertaken every common effort to maintain" a basis for the coalition's continuation, even in the face of what he termed "the skepticism of the whole German press" and skeptics in both governing parties.

But "after the events of the past few days," he said, "I was forced to lose my political trust in some of the leading Free Democratic persons. Continued cooperation can no longer be expected of either the Social Democratic ministers or the chancellor."

Schmidt said that only new elections could ensure a new chancellor and government "full democratic legitimacy."

To bring these on, Schmidt said he was ready to ask for a vote of confidence -- expecting to lose it -- on the condition that the opposition parties agreed to refrain from trying to elect an alternative chancellor in the ensuing 21 days before parliament would be dissolved by President Karl Carstens. The West German constitution allows for this three-week period to give the Bundestag, the lower house of parliament, time to come up with a new coalition if it can.

The chancellor invited the other party leaders to joint talks next week about such a deal.

In a brief reply, Kohl dismissed the offer, saying: "I can see no sense in a talk among party leaders whose actual goal would in the end only be that you prolong the period of your minority government."

Genscher, in turn, also snubbed Schmidt, stating that the way should be left open for "other possibilities" foreseen by the constitution to remove a chancellor that would avoid the "several-month-long period of paralysis" that tolerating a minority government would mean.

This suggested that Kohl and Genscher, assuming they can reach agreement on a new coalition, could try to remove Schmidt by calling for a "constructive vote of no confidence" in the chancellor and simultaneously proposing an alternative candidate, most likely Kohl.

By installing themselves in a new government before scheduling new elections, the conservatives would have the advantage -- which Schmidt was hoping to deny them -- of campaigning with a chancellor already in office and a new center-right platform worked out with the Free Democrats. The Christian Democrats are generally agreed there should be new elections several months after they take over so as to give them a new mandate and a full four-year term.

For the Free Democrats, who are reluctant to face national elections until the next scheduled ones in 1984, this strategy affords at least some time to rebuild political credibility and negotiate a pledge from the Christian Democrats to keep their party as a coalition partner regardless of the election outcome.

Genscher, though, faces stiff resistance from left-wingers in his party to an alliance with the conservatives. A party spokesman disclosed that 18 of the Free Democrats' 53 parliamentary deputies voted against their leader's advocacy of a new coalition at a caucus this morning.

Latest opinion surveys suggest that the Christian Democrats would win an absolute majority with up to 56 percent if a national vote came today. The Free Democrats, in contrast, are running dangerously close to the 5 percent minimum required to take seats in the Bundestag.