The democratic revolution sweeping the world could falter if countries seeking to transform their societies fail to attract investment capital from the developed nations, former Arizona Governor Bruce Babbitt warned Thursday.

"A world that once rejected (foreign) investment has opened its gates, only to find that it's not there," he said.An unsuccessful contender for the 1988 Democratic presidential nomination, Mr. Babbitt described the rejection of Marxism and the democratic movement in Eastern Europe and Latin America as "fragile blossoms" that could wither and die if the new governments in those countries are unable to raise living standards.

The international trading system developed after World War II also should be totally overhauled to permit developing countries to pursue export-driven economic strategies, while nations such as Japan should be required to maintain balanced trade, he said.

He said the United States and Japan are locked in a mutual economic embrace in which Japan invests its surplus capital in an America living beyond its means.

"It's a destructive embrace because it deprives the rest of the world of access to investment capital," he said.

Expectations that West Germany could play a major role in the economic restructuring of Eastern Europe have been dampened as it moves "to fulfill its historic destiny, for better or worse," he said.

Mr. Babbitt, now a partner in the Phoenix office of the law firm Steptoe & Johnson, spoke at a breakfast meeting announcing the launch of a quarterly magazine called Overseas Business.

The magazine will publish its first issue in June and will be distributed free of charge to some 200,000 American business executives involved in international ventures, said T. David Kingston, managing director of Irish Life Assurance Co., a Dublin-based firm that is the principal shareholder in Cara Communications Ltd.

Cara, headquartered in Des Moines, Iowa, will publish the magazine. Mr. Babbitt will serve as a contributing editor.

In his speech, Mr. Babbitt said the world has been dealing with trade frictions in an anecdotal way, with negotiators focusing on questions such as, ''How many knotholes are acceptable in a sheet of plywood?"

Asserting that "it's now time for the leaders of the world to reinvent the trading system," Mr. Babbitt said such a move "will take a leap of the imagination."

Despite America's trade problems with Japan and other rapidly developing Asian economies, their success helped win the Cold War, he said, by showing other countries the value of market-oriented policies.

But by continuing to run trade surpluses, Japan and other Asian nations limit the opportunities for others, he said.

In an interview after his speech, Mr. Babbitt said the trading system is collapsing "because the rules are too vague and the organization is too loose."

The General Agreement on Tariffs and Trade, the Geneva-based body that sets and monitors the rules of international trade, is guided by the concept of fair trade, but fairness is in the eye of the beholder, he said.

"That's at the root of our problem with Japan," he said. "We need to move to a system in which fairness is defined by numbers. Industrialized countries would agree to measures they would take if their current account

balances got out of line."

Mr. Babbitt, who said he has no intention of seeking the Democratic presidential nomination in 1992 but would not rule out another try for elected office in future years, likened the current multilateral negotiations within GATT to "rearranging the deck chairs on the Titanic."