Solomon-like, the State Department made an agonizing choice yesterday between the interests of Eskimos and bowhead whales.

The whales won.

The issue was this:

Last June the International Whaling Commission concluded that the bowhead whale was threatened with extinction and should no longer be killed. The United States was a party to that agreement.

But the Eskimos of Alaska protested that their was of life would be endangered if they were barred from whale hunting.

They found an ally in the Interior Department, which urged that the United States will not now file an objection.

This pleased the Commerce Department, which is anxious to maintain international fishing agreements.

The bowhead whale population is estimated at between 600 and 2,000. The Eskimos last year harvested 43 of the whales and are estimated to have wounded another 79.

The State Department, through the office of Assistant Secretary Patsy Mink, conceded that a ban on bowhead hunting would "cause a sudden disruption of [the Eskimo] way of life." It proposed further talks with the commission in December to try to work out a conservation and research program that will protect the whales while still allowing "substance hunting" by the Eskimos.

Mink said she was hopeful this resolution will come about.

The whales have a large and active political constituency in the United States in various conservation and environmental organizations.