In a gloomy report that could influence the outcome in West Germany's elections Sunday, the government of Chancellor Helmut Kohl announced today that the country's unemployment rate rose in February to a record postwar level of 2.54 million--10.4 percent of the work force.

While the prospects of deploying modern nuclear missiles have aroused heated debate during the campaign, the pocketbook issues of how to revive a weak economy and curtail joblessness--which has grown faster here in the past two years than in any other Western European country--have generated public skepticism that either of the major parties is capable of solving the mounting crisis.

Although stressing that the February report did not produce the "horror figures" some people had expected, Josef Stingl, president of the Federal Labor Office, admitted that "we will look worse at the end of this year than we did at the end of 1982."

Until now, generous welfare benefits have eased the burden of the unemployed. But the next government, regardless of the party that leads it, may face the unpopular task of slashing these payments because of a huge budget deficit and pessimism that increasingly antiquated West German industries can spark a resurgence in exports.

Kohl's Christian Democrats have charged that they inherited a dismal economic situation caused by 13 years of Social Democrat-led governments. A number of opinion polls indicates that this campaign theme has worked, as a majority of people believe the Christian Democrats would prove more adept at handling the economy than their rivals.

Sensing their vulnerability on this issue, the Social Democrats have emphasized the missile controversy more than the economy. But there are signs lately that they are gaining new support with their call for a massive jobs plan and a shorter working week, even though they have not been able to persuade many voters that Kohl bears responsibility for the recent spurt in unemployment.

Kohl's conservative government, whose campaign posters exhort West Germans to "vote for the coming upswing," claimed success today in containing the rise in unemployment.

Labor Minister Norbert Bluem, citing a snap of cold weather as the chief cause in the loss of jobs last month, insisted that "the trend has been broken" and that unemployment "could be reduced step-by-step starting this spring if automobile and housing industries serve as the motor of our upswing."

The opposition Social Democrats, however, argue that the number of unemployed has grown by 750,000 since Kohl took power five months ago. Deputy parliamentary leader Wolfgang Roth described the latest figures as "alarming" and predicted there would be 3 million unemployed by the end of the year unless the Social Democrats' jobs program was adopted urgently.

Kohl's Christian Democratic Union contends that its plan of pumping investment money into auto and construction companies is only now starting to yield results. The Economics Ministry reported Wednesday that industrial output jumped 4 percent, with construction alone showing an increase of 14 percent.

But analysts here predict that such robust signs will fade quickly as investment subsidies taper off. In addition, export orders are dropping under the weight of the lingering slump suffered by the country's trading partners.

Although his government has provided state subsidies, Kohl says he wants to restore more private initiative to the West German economy in order to adapt the country to more intense competition in the computer age. West Germany trails far behind Japan and the United States in such advanced fields as microelectronics.

The Social Democrats, on the other hand, claim that only more government involvement can direct a huge jobs program and drastic overhaul of the economy. They accuse Kohl of seeking to create a society that favors the strong, wealthy class at the expense of the poor.

The Social Democrats also charge that many businesses have conducted what amounts to an "investment strike" by inserting clauses in contracts that would enable them to retract their money if the Social Democrats win Sunday.

The left-leaning Frankfurter Rundschau newspaper reported today on a widespread campaign by companies seeking to influence the votes of their employes with letters and cards bearing messages such as: "Safeguard your future and vote for the Christian Democrats."

The newspaper said several food store chains and banks sent letters to workers saying that layoffs would become unavoidable and many stores would have to close if the unemployment situation worsened--which, they claimed, seemed inevitable if the Social Democrats regained power.

The Christian Democrats, while ostensibly deploring such behavior, frequently observe that the Social Democrats "must ask themselves" why many businesses are acting in such an apprehensive manner.