West Germany's Free Democratic Party, a vital yet vulnerable element in Chancellor Helmut Kohl's new national government, remained badly bruised today at the close of a national convention.

Backed by a narrow majority, party Chairman Hans-Dietrich Genscher was able to push through a new leadership lineup and policy program that reflected efforts to shift his small centrist party to the right.

But acrimonious feuding between the party's left and right wings never let up at the three-day congress here. This bickering resulted in only ambivalent convention support of NATO plans to deploy Pershing II and cruise nuclear missiles in Europe next year and in a highly qualified delegate endorsement of the party's month-old alliance with Kohl's conservative Christian Democratic Union.

Raising the threat of a rupture, dissident party members announced a rump congress Nov. 28 in Bochum to decide whether to form a new liberal party. Several prominent left-wing parliamentary deputies declined to run again for party leadership positions and others were dropped from their posts by the convention. Others announced they were leaving the party.

At issue is how the party can regain the public credibility it lost by switching hurriedly into a new federal coalition with Kohl last month after abandoning Helmut Schmidt's Social Democrats. Since then, the Free Democrats have been defeated in two regional elections.

Survival of the Free Democrats is essential for Kohl, whose own party cannot count on winning an absolute majority in national elections promised for March. The new chancellor needs the Free Democrats to stay in power and to balance the right-wing influence of his other coalition partner, the Christian Social Union headed by Bavarian leader Franz Josef Strauss.

The Free Democrats' swing to the right has reopened the deep rift between opposing left and right branches of German liberalism that were joined when the party was founded in 1948.

The left, which has criticized Genscher for changing the party's alliances to the new coalition and which contends that his low public image now has become an election liability for the party, wanted a new chairman. The left wing also favored a general policy tilt to the left to make sure the party keeps its identity in the new alliance with the conservatives.

Those on the right stood with Genscher, who is also foreign minister, to oppose any change in Free Democratic foreign policy positions and to advocate an economic policy with a new emphasis on less state help and more self-reliance in view of West Germany's economic slowdown.

In a powerful closing speech, parliamentary floor leader Wolfgang Mischnick warned the convention's 400 delegates that continued displays of disunity would drive voters away and forfeit the party's chances of staying in the parliament. He urged members to "stop this intense self-obsession and self-criticism" and pleaded with them to stop hurting the party so that German liberalism could survive.

Also sounding anxious about the party's future, general secretary Irmgard Adam-Schwaetzer declared, "We will win the election fight if we stand together. That must be clear to everyone."

The resurgence of the party's right wing was most evident in elections for the Presidium. Former interior minister Gerhart Baum was the only member of the left wing elected to the top committee, and he was elected by a margin of one vote although he ran unopposed.

In what was perhaps its most radical move, the congress dissolved the party's official youth organization, the leftist Young Democrats, who had threatened to quit anyway if Genscher were reelected chairman. In its place, delegates voted to fund a right-wing rival group, the Young Liberals.

On several major issues, the congress approved seemingly contradictory resolutions suggesting a deep ambivalence about the right course to follow.

It reaffirmed, for instance, party support for the North Atlantic Treaty Organization decision to deploy new nuclear missiles in Europe in late 1983 if U.S.-Soviet negotiation on reducing such weapons fail. At the same time, delegates called for "cooperation with the peace movement," which has opposed the NATO plan.

Heading off other moves that threatened to weaken Free Democratic backing for the alliance decision, Genscher promised that the national party congress next year would have time to review the deployment plans while also considering the status of the U.S.-Soviet arms talks.

The congress also qualified its approval of the new Bonn coalition by censoring the way Genscher handled it and terming the agreement with the Christian Democrats inadequate. Inviting a confrontation with Kohl's party, delegates demanded that the Free Democrats regain control of the Interior Ministry. The party lost the ministry to Kohl's other ally, Strauss, under the new coalition.