West Germany kicked off a two-month election campaign today when President Karl Carstens announced he was dissolving parliament and set new general elections for March 6 that are viewed widely as a referendum on deployment of nuclear missiles here and the increasingly difficult economic situation.

The long-anticipated decision to call elections fulfilled the wishes of the four major parties and Chancellor Helmut Kohl, who deliberately lost a parliamentary vote of confidence three weeks ago in order to seek a stronger mandate for his center-right coalition. Kohl came to power Oct. 1 after the Free Democrats broke with their coalition partners, the Social Democrats, and instead formed a government with Kohl's party, the Christian Democratic Union.

Despite their comfortable lead, the Christian Democrats are heading into a difficult campaign that will involve fierce debate on rising unemployment and the unpopular prospect of stationing intermediate-range nuclear missiles in West Germany beginning in December.

The Christian Democrats also could be hurt by their unswerving fealty to U.S. negotiating positions at the arms control talks in Geneva between the United States and the Soviet Union.

Kohl and other party leaders have said the party is firmly wedded to President Reagan's so-called "zero option" that calls on the Soviet Union to dismantle its intermediate-range nuclear missiles aimed at Western Europe in return for the canceled deployment of Pershing II and cruise missiles by the NATO alliance.

Since former chancellor Helmut Schmidt dropped out as the party's candidate for top office, the Social Democrats have sought to capitalize on strong antinuclear sentiment throughout the country by chastizing the Reagan position as too inflexible to coax a compromise deal with Moscow.

Schmidt's successor as party leader, Hans-Jochen Vogel, also is seen as a more conciliatory figure who could lure back into the Social Democrats' column some left-wing and antinuclear elements who bolted from the party in favor of the Greens, a varied collection of antinuclear and environmental groups.

In the other major campaign issue, Kohl insists that the country's economic slump is due largely to the social welfare policies pursued during 13 years of Social Democratic rule.

But the unemployment level, already at a postwar high of 2.2 million, is expected to climb to 2.5 million by election day, and many analysts believe the Christian Democrats will suffer at the polls as the current party in power.

The emotional intensity of the economic and security issues involved in the campaign has accentuated the uncertainty over the electoral outcome.

In his televised broadcast to the nation, Carstens said he was deeply troubled by constitutional problems inherent in Kohl's contrived defeat in order to induce early elections. West Germany's postwar constitution is designed to prevent the frequent dissolution of parliament and thwart the kind of political instability that brought Adolf Hitler to power 50 years ago this month.

"I will not hide the fact that the objections raised made me think twice," said the president.

But Carstens said he could not ignore the popular desire to hold midterm elections, despite the possibility that "the situation could be more difficult after March 6 than it is at present."

"There is no longer a working majority in parliament to support government policy," he said. "I stand before a situation in which all the parties in parliament--for different reasons--consider new elections necessary."

Opinion polls show that Kohl's Christian Democrat Union and its Bavarian allied party, the Christian Social Union, hold about 48 percent of the vote, while the opposition Social Democrats hover around 40 percent.

Polls show that the Free Democrats have fallen below the 5 percent required for seats in parliament and are threatened with extinction. The Greens currently hold 7 percent and could win seats for the first time in the election.

Some analysts predict that many voters, wary about the marginal status of the Greens and the Free Democrats, will tend to cast their ballots with the large parties rather than see a vote dissipate if one of the small parties failed to earn 5 percent.

Others believe that the Free Democrats could salvage their position in parliament by reasserting their traditional role as a moderating force between left and right, particularly if the Greens are perceived in the waning days of the campaign as holding the potential balance of power.