Voters in towns and tiny villages spread along the vast and frigid coasts of Greenland today overwhelmingly approved a referendum granting home rule to the icy island but keeping it within the Danish kingdom.

Only about 50,000 persons -- about 40,000 native Greenlanders and 10,000 Danes -- live on this 840,000-square-mile island, some 85 percent of which is covered by an ice cap.

Of these, 22,000 Greenlanders and 6,000 Danes were eligible to vote. Local editorials in Danish-language newspapers, however, urged Danes not to vote and to let native islanders alone decide the issue.

With 16,000 votes counted, representing close to 88 percent of the anticipated vote, 70 percent of the voters cast ballots approving the home rule bill, with about 25 percent opposing it. A small number of blank ballots were also filed.

Voter turnout was running at about 62 percent, somewhat lower than anticipated, which could indicate many Danes who live here decided to stay away from the polls.

In any case, there was never any doubt that the measure would be approved.

It will give Greenland roughly the same political autonomy as the Faroe Islands -- another but much smaller north Atlantic community of the Danish crown -- has had since 1948.

The home rule measure, developed jointly by a commission composed of Danes and Greenlanders, is designed to end what Denmark's minister for Greenland, Joergen Peder Hansen, calls "the Danish political dominance" over Greenland yet continue the "solidarity" between the two areas.

The bill clearly grants Greenland greater control over its affairs than ever before. But it is also based on the concept of "national unity."

Thus, Greenland, under the bill's language, remains a constitutent part of Denmark, with ultimate sovereignty continuing to rest in Copenhagen. Absolute jurisdiction in certain fields -- specifically constitutional, foreign and defense affairs and national finances -- also remains with "national authorities."

Greenland has been a Danish colony since 1721 and given the status of a county on equal terms with Denmark in 1953. Yet the situation, until today's referendum, as Hansen points out, "was that in almost all important social affairs in Greenland, the Danish state made all the decisions, passed all the legislation, administered and organized the finances. The Greenlanders tended chiefly to the social sphere."

Under the new bill, political power here will shift to two new elected bodies -- a new Greenland assembly or legislature elected by popular vote and an executive administration elected by the assembly.

Between May 1, 1979, when the measure takes effect, and Jan. 1, 1981, the Greenland local authorities are expected to gradually take over the mammoth island's domestic affairs, taxation and duties, control of the fishing industry, which is the island's largest, control over imported labor, state planning, and legislation dealing with trade and competition, something that eventually could loosen the virtual monopoly that Denmark still maintains on Greenland's commerce.

During the same period, Greenland is supposed to also take over running of a variety of Danish-subsidized areas such as social welfare, church affairs and education.

Beyond 1981, this is supposed to extend to public health, housing, environmental protection and inland transportation.

Denmark will continue indefinitely to pump about $250 million annually into the Greenland economy, which earns only about$100 million annually from exports. But this will be done with bloc grants and local authorities here will handle distribution of the funds.

The bill provides that Greenlandic, a language evolving from the Greenlanders' Eskimo ancestors, be the "principal" language, although a thorough indoctrination in Danish is also called for.

The potentially most importand and controversial provision of the bill in the economic sphere is one that recognizes that the "resident population of Greenland have certain fundamental rights when it comes to natural resources." This refers to possible funds of oil or development of other mineral wealth, such as uranium and molybdenum.