The 38th regular session of the General Assembly opened today under a cloud of U.S.-Soviet tensions, with the dialogue between the two superpowers--an autumn tradition in New York--broken off.

In a glum prelude to the session, Secretary General Javier Perez de Cuellar said that "great divisions, enmities and hostilities exist in the world community," and added: "That is precisely the condition in which direct contact at the highest possible level is essential."

He was referring to the cancellation of Soviet Foreign Minister Andrei Gromyko's U.N. trip in a dispute over landing rights in the New York area that followed the Soviet downing of a South Korean passenger plane.

Indian Prime Minister Indira Gandhi, on behalf of the 101-nation Nonaligned Movement, had sought to turn the session into a global summit meeting. "At a time of great distrust between the superpowers," said an Indian official, "talks like these might help to diffuse tensions."

But although President Reagan is to address the assembly on Monday, he has declined the invitation to attend either of the two two-hour "mini summits" that are to take place next week here.

So far, Indian diplomats said, 26 countries had committed their leaders to attend. Those listed as accepting include President Francois Mitterrand of France and Prime Ministers Pierre Trudeau of Canada and Olof Palme of Sweden. Austria, Finland, New Zealand, Hungary and Poland are also said to have accepted.

The object, the Indians say, is to foster an informal dialogue--without agenda, records or final communique--similar to the more restricted summit meeting on economic relationships between the Third World and the West that took place two years ago in Cancun, Mexico. Without American or Soviet participation, however, there is little expectation that anything worthwhile would result.

The assembly began today with the election of Panamanian Vice President Jorge Illueca to the prestigious but largely ceremonial post of assembly president.

Delegates are to begin Wednesday to approve a proposed agenda of 142 items, most of them U.N. regulars on which little new ground is likely to be broken by the assembly's nonbinding rhetoric.

On Friday, newly independent St. Kitts-Nevis is to be admitted as the 158th U.N. member.

In the eyes of most diplomats, the most valuable aspect of the three-month long session is the opportunity for national leaders--on the level of foreign minister and above--to meet informally, or even secretly, in a round robin of bilateral discussions.

For many countries, these meetings prove more valuable than a staged summit, and it is there that Gromyko's absence will be felt most strongly.

Diplomats from many smaller countries say they had been hoping to tell both the American and Soviet foreign ministers privately that the most disturbing thing is the confrontational atmosphere between the two superpowers.