In the biggest one-time response to three decades of American pleas for the reuniting of divided families, the Soviet Union has promised to allow 117 of its citizens to join relatives in the United States, the State Department announced yesterday.

If the Soviets make good on the promise, it would clear up 36 of the 126 divided-family cases whose resolution the Reagan administration has been seeking as a sign of Moscow's commitment to easing tensions with the United States.

Department spokesman Charles Redman praised the Soviets' stated intention as "a positive step that will contribute to an improved atmosphere in our relations." However, he stressed that the United States believes there still is a lot of room for improvement in Soviet emigration practices, which have become markedly more restrictive in recent years. Other U.S. officials said privately that it is too early to tell whether the Soviet action signals a shift toward a liberalization of Moscow's decades-old reluctance to let its citizens emigrate freely.

Redman said that Soviet officials informed the United States of the decision on Monday "in the closing hours" of an otherwise inconclusive meeting in Bern, Switzerland, about human rights issues.

In addition to these 117 people, Redman said, the Soviets also promised to permit emigration of two other people who fall into different categories, one involving the spouse of a U.S. citizen and one involving an individual with dual nationality.

Department officials said that because of Privacy Act considerations and a desire to avoid confusion, the names of the persons involved would be withheld until their families are notified. The officials said that is expected to take about three days, and they cautioned that even if the Soviet government takes quick action, it probably will be several weeks before the people involved receive permission to leave the Soviet Union.

The officials said privately that the mother, brother and other family members of Jewish dissident Anatoly Shcharansky, who was released in an East-West prisoner exchange earlier this year, are not on the new list of people to be allowed to emigrate. The officials noted that the latest Soviet move applies only to those with relatives living in the United States, while Shcharansky's family members are in the category of Soviet Jews seeking to emigrate to Israel, where he now resides. U.S. officials have said that the Soviets gave assurances that Shcharansky's relatives would be allowed to emigrate at the time they made the deal to swap him for Soviet bloc spies held in the West.

In addition to its efforts on behalf of more than a million Jews whose applications for exit permits have been denied, the United States has pressed Moscow for almost 30 years to liberalize emigration policies, particularly as they apply to people with U.S. family ties.

Redman said the United States maintains three lists of people meeting those criteria. At present, he added, there are 126 cases of divided families, 21 cases of separated spouses and 20 dual national cases. Other department officials said later some individuals are on more than one list.

President Reagan has put particular emphasis on signaling to the Soviets that their actions on emigration questions will be a factor in moves to improve relations. At their summit meeting in Geneva last November, Reagan and Soviet leader Mikhail Gorbachev agreed to cooperate in resolving cases involving humanitarian factors. Redman said yesterday that the new Soviet gesture "give[s] real meaning to the [Geneva] statement."

Following the summit, Gorbachev promised to dispose of 33 divided family cases, and Redman said that the people covered by 24 of those cases already have left the Soviet Union.

Both the Soviet Union and the United States are among the 35 signatory nations to the 1975 Helsinki accords on security and cooperation in Europe, and the United States has criticized Moscow frequently for failing to observe the agreement's endorsement of human rights principles, including free emigration.