In the wake of his triumphant success in the West German elections, Chancellor Helmut Kohl sought today to stifle a bitter quarrel within his ruling coalition over who will serve as the new government's foreign minister.

At a news conference today, Kohl tried to quell speculation about a serious rift among his coalition partners and said negotiations over Cabinet posts would not begin until after state elections Sunday in Schleswig-Holstein.

Hans-Dietrich Genscher, the leader of the small liberal Free Democrats, has been foreign minister since 1974 and insisted that his party's surprising recovery at the polls had earned him the right to retain the post.

But Franz Josef Strauss, the 67-year-old head of the Christian Democrats' sister party in Bavaria, the Christian Social Union, contended that his party's strong showing also warrants a key position in the next government.

Strauss flew to Bonn today from his Munich headquarters to hold exploratory talks with Kohl and Genscher about the distribution of power among the governing parties.

Before the election, Kohl was known to have felt apprehensive about the prospect of his conservative alliance winning an absolute majority that would virtually cede the posts of vice chancellor and foreign minister to his ambitious rival, Strauss.

He was clearly elated by the turnabout in the Free Democrats' fortunes and favors granting the job once again to Genscher, who is a close personal friend.

The Free Democrats, who held four posts in the previous government, would probably be willing to sacrifice the agriculture and justice portfolios if they can keep the foreign and economics ministries.

Strauss warned today, however, that Genscher should not seek to press his party's results. "The tail should not wag the dog," he said. "The Christian Social Union will not do this and we recommend that the Free Democrats not do so."

While refusing to comment on the distribution of posts within his Cabinet, Kohl repeated his plans for a broad ruling consensus when he told a press conference, "We asked for a yes to our coalition policies of the political center and we are satisfied that we have got it."

Kohl's ability as a national leader has yet to be tested, though the forthcoming coalition negotiations may provide the first real challenge.

In contrast to such predecessors as Helmut Schmidt, Kohl lacks expertise in finance and foreign affairs, nor does he possess the stature of Konrad Adenauer or Willy Brandt.

Yet his prowess as a party organizer and campaign strategist were clearly demonstrated by the Christian Democrats' extraordinary victory.

In a decade as party leader, Kohl has more than doubled the membership rolls and built an effective populist base for the Christian Democrats, drawing support from a wide range of constituencies including big business, church groups and increasingly, blue collar workers.

The Christian Democrats scored their most dramatic gains yesterday in former Social Democratic strongholds, including northern industrial areas like the Ruhr steel belt.

Many of these workers, whose hefty paychecks have nurtured middle class notions of political and economic stability, have become convinced that the conservatives are more adept at handling financial and unemployment matters than their traditional patrons, the Social Democrats.

Several analysts said today that up to 1.5 million people who normally vote for the Social Democrats shifted in this election to the Christian Democrats.

In that regard, Kohl's personal decision to change party slogans a few weeks ago to encouraging, positive phrases such as "Upward with Germany" and "Vote for the upswing" is considered to have induced many workers, deeply worried about a record 10.4 percent unemployment rate, to cast their ballots for the Christian Democrats.

Kohl said today that he was most gratified by his party's powerful showing in Protestant, industrial regions in the north--where the Social Democrats are supposedly dominant.

"This result has set our party back several years," admitted a Social Democratic official. "We will have to rebuild by winning workers back from the Christian Democrats before we can think of holding power again."

The Social Democrats today nominated their defeated candidate for chancellor, Hans-Jochen Vogel, to become the new opposition parliamentary leader replacing the ailing, 76-year-old Herbert Wehner.

Despite their worst result in more than two decades, many Social Democrats felt that Vogel conducted a good campaign and succeeded beyond most expectations in uniting the party's left and right flanks.

Vogel has pledged to lead "a constructive opposition" party, but it is still open to speculation whether the Social Democrats will move further to the left, to recapture antinuclear elements lost to the Greens, or try to reclaim the middle-class working vote.

Several voluble left-wing Social Democrats lost their seats in parliament in the massive defeat, perhaps a blessing for Vogel if he decides to shift the party back toward the center.

But former chancellor Schmidt, the strongest voice on the party's right who still ranks as the country's most popular politician, said today that he is resigning as party vice chairman to devote more time to private pursuits.

Schmidt's diminished role deprives the party of one of its most forceful moderates, whose ideas on defense and the economy still command respect throughout the country.

Politicians and diplomats here predict that, barring any early signs of progress in arms control talks at Geneva, the Social Democrats are likely to become more vehemently opposed to the prospective deployment of modern nuclear missiles later this year.

The radical Greens party, which will enter parliament for the first time, holding 27 seats, announced today that it will conduct a series of nonviolent protests to prevent stationing of the missiles.

Marion Maren-Griesbach, a member of the Greens' executive council, said that the missiles would be contested with "hunger strikes, sit-ins at American military bases, demonstrations and silent marches."

The Greens' chairman, Rainer Trampert, welcomed his party's "historic" accession to the Bundestag but described Kohl's victory and his firm support of U.S. plans to deploy the new missiles if the arms talks fail as "a catastrophe for West Germany."