West German Free Democratic leader Hans-Dietrich Genscher's effort to keep his small party intact, while aligning it with the conservatives to form a government, encountered a new obstacle when a fourth regional branch of the party called for an emergency national congress to consider the coalition move.

Bremen's Free Democrats joined last night with branches in West Berlin, Hamburg and Schleswig-Holstein to demand a convention, thus forcing the party leadership under existing rules to summon one. The grassroots push suggested widening resistance to Genscher's efforts to swing his centrist party quickly into alliance with the conservative Christian Democratic and allied Christian Social parties after abandoning a 13-year coalition with Chancellor Helmut Schmidt's Social Democrats last Friday.

An opinion poll taken this week by the Allensbach Institute indicated that support for the Free Democrats has plummeted to 2.3 percent, down two or three percentage points since the coalition's breakup five days ago.

The poll, commissioned by the paper Die Zeit, showed that support for the Social Democrats has risen, increasing by about five percentage points to 36.8. The Christian Democrats continued to draw an absolute majority, with 52.7 percent.

The evident erosion of popular as well as party backing for Genscher's course prompted doubts about whether the former foreign minister would be able to deliver the minimum of 23 votes needed from his 53 members of the lower legislative house to bring off a planned Oct. 1 move to topple Schmidt's minority government and install a new center-right coalition.

Free Democratic Party leaders, contending that rapid formation of a new government is essential to consolidate the 1983 budget, insisted that negotiations with the conservative parties would proceed and that the no-confidence vote against Schmidt would be called next week as agreed.

Genscher told reporters the request for a special party congress was "a legitimate demand" but he said it could not be allowed to interfere with the timetable for setting up a new government. Other party officials stated that according to party statutes the special convention would not be convened until mid-October.

A national congress has long been scheduled for Nov. 5 in Berlin. Initially, Genscher was reported to have been planning to pull his party out of the badly strained coalition with the Social Democrats shortly before that congress, then ask backing for a coalition with the conservatives.

But Schmidt's preemptive call for immediate national elections upset this orderly scheme. Genscher is now left having to justify not only the party's swing to the conservatives but also the hastiness with which it is happening.

Reflecting the fierce opposition he faces, especially from the party's left wing, Free Democratic deputy Helga Schuchardt today described Genscher's changeover as "a coup from above." She told reporters, "It is not we who are splitting the party but those who got us into this situation."

Meanwhile, the Social Democrats have stepped up their characterizations of Genscher as a betrayer and political opportunist, while attempting to woo disenchanted members of his party.

Ex-chancellor Willy Brandt, chairman of Schmidt's party, charged in a newspaper interview that a conservative government would be too soft toward the United States, bowing to U.S. demands on issues such as the Soviet pipeline. United Press International reported from Bonn.

Genscher might answer his critics by emerging from the coalition talks with enough of a compromise program to claim that he has upheld his party's reform tradition. But compounding his task are state elections in Hesse Sunday. If they go against the Free Democrats, as widely predicted, Genscher's already weak negotiating position could be affected.