The United States and Britain reacted cautiously yesterday to announcement of an internal Rhodesian settlement that will lead to black rule by the end of the year.

"We are not rushing to embrace or reject this agreement," State Department spokesman Hodding Carter III said.

He called the agreement a new stage in the process of political change in Rhodesia, but said the United States needed more details on who would hold power during a transition from white to black majority rule.

In London, British Foreign Secretary David Owen called the settlement a significant start toward an acceptable solution, but said he hoped the pact between Prime Minister Ian Smith and three black leaders could be widened to include the so-called Patriotic Front.

The two leaders of the front, Robert Mugabe and Joshua Nkomo, have engaged in discussions on the future of Rhodesia with the United States and Britain, but have refused to take part in the internal Rhodesian negotiations.

In a clear reference to the fact that Mugabe and Nkomo have an estimated 16,000 armed guerrillas under their command, U.S. Secretary General Kurt Waldheim warned yesterday that the Rhodesian problem would not be solved "as long as some are excluded from that process.

Waldheim voiced fears in a statement that "the conflict will continue, with grave consequences for peace in the area.

Opposition to the internal Rhodesian settlement also continued to build among black African countries at the United Nations, where delegates have demanded a Security Council meeting "as soon as possible" to discuss the session.

British Ambassador Ivor Richard, this month's president of the Security Council, stepped up consultations in preparation for a council debate on Rhodesia now expected to start late Monday. U.S. Ambassador Andrew Young cancelled a planned trip to Southeast Asia in order to be able to attend.

One source of potential concern to many observers is that a continuation of the guerrilla war carries with it the possibility of increased involvement by the Soviet Union and Cuba.

The official Soviet news agency Tass said yesterday that the internal Rhodesian agreement created conditions for new and dangerous international tensions in Africa.

In Capetown, South African Prime Minister John Vorster welcomed the internal settlement but said its success would depend whether the country was let alone to determine its own future.

"How successful it will be in practice will depend, on the one hand, on the good faith with which the parties adhere to and implement it in practice, and, on the other hand, whether they are allowed by so-called 'public opinion' as well as African and world organizations and countries, neighboring and far away, to arrange and determine their own affairs according to their own wishes.

"Time alone can give the answer to this," he said.