Chancellor Helmut Kohl's center-right government won a resounding victory in the West German parliamentary elections today, vindicating his call for a mandate to strengthen his country's ties to the western defense alliance and to pursue more free-market initiatives to revive the economy.

The convincing triumph by West German conservatives, who sent the opposition Social Democrats to their worst defeat in more than two decades, evoked relief in western capitals and business circles here. President Reagan and British Prime Minister Margaret Thatcher telephoned their congratulations to Kohl upon learning of his confirmation as chancellor.

"This was a clear-cut victory for politics of the center," Kohl declared as he was cheered by jubilant supporters at Christian Democratic headquarters. "I expected a good result and it turned out that way."

Kohl's conservative alliance of Christian Democrats and the Bavarian Christian Social Union won 48.8 percent of the vote, just short of an absolute majority and an improvement from the 44.5 percent they received in the 1980 elections.

The junior partner in Kohl's ruling coalition, the Free Democratic Party, rebounded strongly in the last weeks of the campaign to capture 6.9 percent, down from 10.6 percent in 1980, and to retain its crucial swing role among West German political parties. Kohl said he would open negotiations with the Free Democrats on Monday to decide on the sharing of Cabinet posts.

The election results also put the antinuclear, environmental Greens in the parliament for the first time with 5.6 percent of the vote.

The opposition Social Democrats plummeted from 42.9 percent in 1980 to 38.2 percent today, losing 27 seats in the Bundestag, the lower house of the West German parliament. "There is no getting around it," conceded the party's candidate for chancellor, Hans-Jochen Vogel, "we have suffered heavy losses. This is a serious defeat."

The Greens, who received 1.5 percent of the vote in 1980, won 27 seats. But the severe losses inflicted on the Social Democrats nullified the Greens' chances of holding the balance of power and seemed to consign them to a marginal role in parliament.

"We had hoped for a different distribution in the Bundestag, one that would have allowed us to tolerate a minority government of Social Democrats," said the Greens' chairman, Rainer Trampert. "That's why we view the result with one eye twinkling while the other is crying."

Appearing on television after his victory was announced, Kohl said his government's first priority was "reducing unemployment and revitalizing the economy."

He also said that the coming year was crucial for security policy and that his government "would use all the power that we have" to help the United States reach an arms accord with the Soviet Union limiting medium-range nuclear missiles in Europe.

"We hope that our American friends, with our trust and support, will be able to come to a result which makes it possible to make peace with fewer and fewer weapons," Kohl said. "But if there is no agreement in the Geneva talks , we are prepared to deploy new missiles later this year."

Kohl added that his government "would be satisfied with solutions on the road to a final goal, which remains, if possible, no American rockets and no Soviet rockets in Europe."

Petra Kelly, a leader of the Greens party, declared that as new members of parliament one of the Greens' primary goals would be "to work together with the Social Democrats to prevent any deployment by NATO of new nuclear missiles."

If Kohl proceeds to form, as expected, a broad ruling coalition linking the Christian Democrats with the Free Democrats, he will be able to count on a 29-seat majority in the 498-seat parliament.

A key question in the aftermath of the elections is whether Franz Josef Strauss, the leader of the Christian Social Union, will seek to become foreign minister, replacing the Free Democrats' leader, Hans-Dietrich Genscher.

Strauss decribed his Bavarian party's 10.6 percent of the vote as "a sensational record result, the best since 1949." But he refused to comment on whether he would try to translate the Christian Social Union's strong showing into control of the Foreign Ministry.

During the campaign he strongly attacked the Free Democrats for their record in foreign affairs and economics in 13 years of sharing power with the Social Democrats.

The Free Democrats, who trailed badly throughout the campaign and risked falling short of the 5 percent of votes needed to hold seats in parliament, greeted their salvation with relief.

Nonetheless, their role will probably be diminished in the next government if Genscher is forced to leave the Foreign Ministry in favor of the ambitious 67-year-old Strauss.

For the embattled Social Democrats, Kohl's comfortable majority will probably mean an extended period in opposition that could revive feuding between left and right flanks that was carefully held in abeyance during the campaign to present a facade of party unity.

"I ask all Social Democrats not to hang their heads now," said Vogel as he conceded his defeat barely one hour after the polls closed. "We must now try to play a constructive opposition role."

The Social Democratic Party's leader, Willy Brandt, said that "some Social Democrats will be disappointed with our results, but we must accept our opposition role for now and later we will come again to power, as we have done before."

Brandt explained that the Social Democrats suffered from the same ravages, in troubled times for the world economy, that brought down other ruling parties in Europe in recent years as discontented voters chose change.

"In our difficult economic situation, many people wanted to believe what Kohl was telling them," he said. "In the coming years, the Christian Democrats will have to prove they can eliminate unemployment and improve the economy as well as they say they can. We can only hope this is true."

The midterm elections were called five months ago, after the Free Democrats broke off their ruling partnership with the Social Democrats to form a coalition with Kohl's Christian Democrats.

Some Christian Democrats, including Strauss, were convinced that they could win an absolute majority last autumn and argued for immediate elections after the collapse of Helmut Schmidt's government.

But Kohl clearly preferred to form a broad, center-right alliance with the Free Democrats, whose popularity plummeted after their controversial switch in coalition partners.

To give the Free Democrats more time to recover support, Kohl brokered an unusual compromise that called for his interim government to deliberately lose a vote of confidence that set the stage for today's elections.

The two-month campaign, scrutinized with intense interest at home and abroad, was considered by many West Germans to be the most bitterly contested election in their nation's 34-year history.

The prime issues were the economy, which has suffered from three years of deep recession that has created record unemployment, and the prospective deployment of new nuclear missiles later this year if arms talks between the United States and the Soviet Union make no progress.

The Christian Democrats blamed their Social Democratic rivals for "gross mismanagement" that led to huge budget deficits and a depressed economy in the latter years of their long term in power.

The Social Democrats countered with the argument that Kohl's efforts to restore more private initiative masked a "socially unjust" policy that aided the rich at the expense of the poor.

They claimed that during Kohl's five months in power, more than 750,000 people lost their jobs. The Christian Democrats, however, contended that their prescriptions to revive the economy could not possibly work within such a short time.

While public opinion polls showed that a majority of West Germans were more concerned about the economy than any other issue, there appeared to be widespread public skepticism during the campaign that either of the major parties knew of sure-fire panaceas to cure unemployment and revive the sluggish growth rate.

In contrast to ambivalence about economic policy, the country has appeared more deeply split over the missiles controversy, which aroused impassioned debate during the campaign.