HARARE, Zimbabwe (AP) _ African leaders are showing more and more concern about population growth on their continent, where large families have been a tradition for centuries and a symbol of prestige and wealth.

The population growth rate is around 3 percent, the highest of any region on the world.

Left unchecked Africa's current population of 550 million people could swell to 877 million by the turn of the century, l.6 billion by the year 2025 and 3 billion by 2050, according to Dr. Frederick Sai, senior population adviser for the World Bank.

The chief concern of Africa's leaders is that overpopulation retards development and perpetuates poverty.

Judging from recent impassioned pleas by the leaders for birth control, family planning is no longer the taboo topic it has been in the past because of desire of Africans to have large families.

The need to curb Africa's population growth figured prominently in at a recent meeting of African parliamentarians here in Harare and at the U.N. General Assembly's special session at the end of May on Africa's economic plight in New York.

''Solutions must be found for population control to avert a demographic catastrophe,'' Zimbabwe's National Assembly speaker, Didymus Mutasa, told about 250 legislators from 37 African nations who had gathered in Harare.

Only in recent years have African leaders publicly acknowledged that many of their major problems - food shortages, unemployment, migration and inadequate education, health and housing facilities - are directly linked to the population explosion.

Food resources and social services have become severely strained as governments try to cope with ever burgeoning numbers of people.

The magnitude of the problem was bluntly put recently by President Daniel arap Moi of Kenya, which has the world's highest population growth rate, around 4 percent a year.

''Every year in Kenya we have to produce enough food to feed an additional 1 million people,'' he said.

''If the population growth continues at the same rate the country will require twice as much food in the year 2000. We have no choice, neither do we have the time to make choices. We must therefore reduce our population growth now.''

It is estimated that Kenya's population has grown to about 17 million since the last census in 1979, when population was 15.3 million.

In Nigeria, Africa's most populous nation, officials readily acknowledge that they don't know how many Nigerians there are. Estimates range from 80 million to 115 million. But a senior government planning official said a population awareness campaign is being prepared.

For centuries in Africa, the worth of a woman and the virility of a man were measured by the number of children they produced.

From a practical standpoint, Africans wanted large families so that the offspring could help tend fields and livestock, bring in extra income and care for parents in old age. Large families were also insurance against a high mortality rate.

At the U.N. session on Africa, Sir Geoffrey Howe, Britain's foreign secretary, reflected the views of many African leaders when he noted that rapid population growth impedes development.

''How is such a population growth to be reconciled with decent living standards?'' he said.

The Harare conference ended with unanimous recognition by the lawmakers that unchecked populations retard development and with a pledge to expand family planning programs.

''There's been an explosion of progress here,'' said Rep. James H. Scheuer, D-N.Y., chairman of the New York-based Global Committee of Parliamentarians on Population and Development, which organized the conference jointly with the Zimbabwe Parliament.

Scheuer recalled that 10 years ago, while touring Africa to advocate birth control programs, he was denounced in one country as a ''genocidal maniac.''

Some of the statistics presented to the Harare meeting provided reasons for the turnabout in attitudes:

-While Africa's population grows at 3 percent annually, food output increases at 1.9 percent a year, forcing governments to spend meager export income on grain imports.

-One in five able-bodied Africans has no job or is underemployed.

-Half of Africa's people are impoverished.

''As long as development lags behind population growth, we can rest assured that we will remain in the vicious cycle of poverty for years to come,'' Zimbabwe speaker Mutasa told the legislators.

''Hunger and malnutrition are most prevalent in the developing world where birth ratios are high and the majority of people live in poverty.''