United Nations, N.Y. — The world will be watching this week to see if a new third force between the superpowers can be stitched together. Between 30 and 40 world leaders are gathering here for two discussion sessions, with Indian Prime Minister Indira Gandhi in the chair. Among the nations present will be France, Sweden, Finland, Austria, Tanzania, Egypt, Morocco, India, Hungary, and Yugoslavia.
No immediate, concrete results are expected to come out of the meetings. Rather they are to be informal and freewheeling, like those of the Commonwealth gatherings.
''Cold warriors, ideological crusaders, and cynics may sneer at Mrs. Gandhi's mini-summit,'' says one Western ambassador here. ''Stalin once asked how many divisions the Vatican had at its disposal. Ideas are, however, powerful. Men want peace and progress.
''The Gandhi summit could well have unintended results,'' he went on. ''Moderates of the Eastern and Western blocs could realize that they have more in common than they have with their respective leading superpower. Moderate nonaligned, moderate communists and capitalists could realize that to some extent at least they are like-minded.''
Originally, when Mrs. Gandhi launched her project at the summit meeting in Delhi last March of governments belonging to the ''nonaligned'' movement, it was hoped that perhaps 60 to 70 heads of state would turn up for the Gandhi gathering. Some even hoped that Presidents Reagan and Andropov might attend and meet each other here.
The worsening of East-West relations after the downing of the Korean airliner has soured some of these high expectations. The Gandhi summit has become ''futile,'' according to some diplomats. It is ''the more timely,'' according to others.
One Asian diplomat refuses to be dismayed. ''A new, informal force could emerge here with some third-world countries, some East European, some West European, which oppose global polarization and intensification of the cold war, which are for dialogue and for strengthening the role of the United Nations,'' he says.
President Francois Mitterrand is expected to call for the right of nations to self-determination; for linking disarmament and development; for not involving the third world in East-West rivalries; and for steps aimed at gradually weakening the influence of the military on both sides of the fence. Mrs. Gandhi is expected to plead for conciliation and cooperation, East-West and North-South , instead of saber-rattling and selfish entrenchment.
Nigeria, Mexico, Brazil, Australia, China, Japan, West Germany, Algeria, and Romania will not attend the meeting. But they are watching it closely and could to various degrees feel attracted to the idea, many diplomats here believe.
''A seed may be planted at the Gandhi summit which may come to fruition only in a few years,'' says one analyst here. ''It would be a mistake for the United States and for the Soviet Union to dismiss this gathering as just another exercise in naivete.''