AEG-Telefunken, the long-ailing West German firm further threatened by President Reagan's decision to extend sanctions against the Soviet gas pipeline project, received emergency support from the government today to avoid financial collapse.

Despite traditional reluctance to aid problem firms, the Bonn Cabinet said it would grant $243 million in loan guarantees to cover specific major capital equipment orders won by AEG abroad--including pumping stations for the projected Soviet pipeline.

The rescue action has little precedent in West Germany. Announcing it, Economics Minister Otto Lambsdorff stressed that the government expects AEG's management and bankers to retain full responsibility for saving the firm. But with a number of once-strong companies faltering across Europe, Bonn's move could affect petitions elsewhere for federal and state help.

Lambsdorff said the government had decided to bail out AEG in the interest of protecting the reputation of West German exporters and to guard AEG's suppliers against the consequences of a possible collapse.

The prospect of job losses for a number of the nearly 100,000 persons employed here by AEG--the country's second-largest electrical firm--is also thought to have been a powerful political incentive for Bonn's shaky left-center coalition to get involved.

The move reflected growing pressure on European governments to bail out companies struggling against the conditions of a prolonged economic recession. In West Germany, the number of firms going bankrupt reached a postwar high last year, and recently published statistics suggest that the number of insolvencies this year will be higher.

Paralleling the rise in failing companies has been an increase in Europe's unemployed. The jobless rate for the 10-member European Community is expected to reach 9.2 percent this year compared with 6 percent two years ago. West Germany reported 1.65 million jobless in June, or 6.8 percent of the work force--the country's highest June unemployment rate since 1950.

As a general rule, the Bonn government has refused aid to failing firms in keeping with its strong free-trade, free-market philosophy. Exceptions involving subsidies to the shipbuilding, coal and steel industries have been justified usually on regional or strategic grounds. Lately, however, rising bankruptcies and unemployment are causing federal and state governments to review policies toward troubled firms.

The federal loan guarantees to AEG are conditioned on the company's banks providing an additional credit line of $110 million.

The rescue package should give the company desperately needed breathing space to realize an ambitious restructuring plan. The plan calls for separating the company's profitable capital goods business into one operating company and its loss-making home appliance and consumer goods business into another.

The rescue operation has been complicated by Reagan's decision last month to deny European firms the use of U.S.-developed technology in meeting contracts for the planned Soviet gas pipeline from Siberia to Western Europe.

The U.S. move is threatening to force AEG to default on a $243 million contract to supply 47 turbines to the Soviet Union. The turbines, used to push gas along the 3,600-mile line, were to be built at an AEG subsidiary's plant in Essen using specialized rotor blades supplied by General Electric.

Shipment of the blades has been blocked by Reagan's embargo. So has the option that a French firm, Alsthom-Atlantique, could manufacture them under a GE license.

Objecting sharply to Washington's extension of the pipeline sanctions, West German Chancellor Helmut Schmidt has argued that the ban stands to hurt West European firms more than the Soviet Union--and this at a time of economic strain in Europe.

The U.S. embargo, on top of AEG's generally deteriorating position, pressed the firm's management to unveil its rescue plan and approach the government for help. The company initially asked for federal and state guarantees totaling $630 million. Talks between AEG and officials in various West German states are continuing.

But AEG's troubles long predate the pipeline embargo. The company has come so close to becoming Germany's largest corporate failure since World War II because of a combination of some costly, misguided ventures and rescue schemes that failed to catch up to past management mistakes.

AEG has been a household name in Germany for generations. Its appliance goods are part of the daily experiences of millions of West Germans. Some of its more successful ventures earlier this century played a major part in the electrification of the country, from streetcars to television.

In the 1960s, anxious to challenge Siemens, West Germany's largest electrical concern, AEG expanded boldly into such fields as construction and shipbuilding. But its string of acquisitions never were properly consolidated, particularly in household appliances. In consumer electronics, the company failed to gain the volume to compete effectively in world markets.

In the 1970s, AEG lost large sums in its involvement in the nuclear power industry. By 1973, AEG stopped paying a dividend, as its corporate reserves were spent.

Finally in 1979, a 24-bank consortium and a group of insurance firms stepped in with a plan to infuse the firm with fresh funds in hopes of protecting their loans. The banks ended up holding 50 percent of AEG's stock, which decreased sharply in value.

AEG stock, which sold for $60.70 when issued new in 1979, closed yesterday at $12.45. It rose slightly today following news of the loan guarantees. The company's operating losses last year totaled $256 million.

The 1979 strategy was for a private enterprise rescue that would eschew all temptations to call for state aid. Company and bank officials blame its failure in part on West Germany's recession lasting longer than expected and interest rates staying relatively high.

The company's employes have called for the government to take a share in the company, a potential move that Schmidt and other senior officials have shunned. Saving AEG, Lambsdorff said today, "is not the business of public authorities."