he United States and four allies today announced a new phase in their effort to arrange the long-delayed independence of mineral-rich Namibia from South Africa, saying their timetable calls for definitive movement by the end of 1982.

The foreign ministers of the Western "contact group"--the United States, Britain, Canada, France and West Germany--made the announcement after Assistant Secretary of State Chester A. Crocker reported on meetings with South Africa's senior career diplomat, Brand Fourie, this week in Zurich.

The statement said the contact group will start discussions with the African parties next month on "proposed constitutional principles" for an independent Namibia "as well as a timetable and an approach to other remaining issues."

Namibian independence is a central point of international concern in southern Africa. South Africa ruled the area, a former German colony, under a 1920 League of Nations mandate that the United Nations revoked in 1966.

Independence would transfer the balance of power from 90,000 whites to 1 million blacks.

The result of Crocker's meeting in Switzerland, according to a senior State Department official who briefed reporters, was a message from South Africa that will permit the contact group to resolve the issues step by step.

The official, who declined to be identified by name, described the main issues as follows:

* Constitutional principles. These would be designed to reassure Namibia's white minority and apparently would include political as well as property rights. The contact group can only "suggest" such guarantees, since an elected assembly is to write the constitution.

* Arrangements for the elections and other procedures for the transfer of control.

* Security arrangements such as the size, makeup and mandate of a U.N. police force during the transition, and the question of U.N. impartiality, which South Africa has challenged.