OTTAWA, DEC. 3 -- Responding to growing demand, the Canadian government today announced an ambitious $4 billion program to double the number of spaces at day-care centers over the next seven years.

The initiative, which is designed to create room for an additional 200,000 children by the mid-1990s, will include operating grants to centers and subsidies to help nonprofit child-care groups build or buy facilities.

The plan also calls for tax adjustments to provide more relief for working parents with middle incomes, especially those with children under the age of 6, and a modest tax break for families with mothers who choose to stay at home. Poor families already receive substantial government aid for child care.

The initiative, which requires approval by Parliament and negotiations with the country's provincial governments, has been studied for nearly two decades and was strongly promoted by women's organizations.

Aides to Prime Minister Brian Mulroney said they hoped the program, promised in his election campaign three years ago, would help lift Mulroney's popularity when he faces voters again before the end of 1989. Mulroney's party dominates Parliament, which is expected to pass the measure.

Critics have complained that the plan gives Canada's provincial governments some discretion in spending the federal funds and that the program's size still falls short of the need.

While the plan calls for services for more than 400,000 children, advocacy groups contend that an additional 1.5 million youngsters require day care. Health and Welfare Minister Jake Epp denied that the number was that high, but he declined to give his own estimate.

Under the plan, tax deductions for child care for children aged 6 and under would double, to $3,000 per child. The deduction for children 7 to 14 would remain at about $1,500. An existing $6,000 ceiling on deductions would be lifted, which would help larger families.

The U.S. tax code provides a 30 percent tax credit on annual child-care expenses up to $2,400 per child, or $4,800 for two or more children.

Unlike many Americans, Canadians have an abiding faith in the ability of government to solve social problems. They seldom gripe about paying higher taxes than U.S. residents in order to support an array of social programs, including an expensive but highly regarded universal health care system.

Barbara McDougall, Mulroney's minister responsible for the status of women, said the new child-care initiative "is vital to the government's recognition of the important role women play in the economy of their individual families and of Canada as a whole.

"The National Strategy on Child Care," she added, "has been designed in the context of values that we as a government support: that economic equality encourages social equality; that Canadians are able to choose the service that is most appropriate for them, and, therefore, that they are best served when government gives them those choices rather than restricts their ability to choose for themselves."

One feature of the proposal admired even by critics is a special $75 million fund for research and development on special child-care problems faced by shift workers and rural and native parents. The government also expects to use some of the money for programs to train and improve child-care workers.

As in the United States, there has been a rapid rise over the past decade in the number of Canada's working women. In 1976, fewer than one-third of mothers with children under 3 worked. Now well over half do. More than two-thirds of those with children in grade school and junior high school hold jobs.

Canada already has several programs for families. A "baby bonus" provides monthly payments of nearly $300 to all families with dependent children under 18, and tax deductions for child-care expenses have been raised in recent years. Government unemployment insurance provides maternity benefits of up to 60 percent of previous income for a 15-week period before and after childbirth.

Under another program, the five-year-old Canada Assistance Plan, the federal and provincial governments subsidize day care for low-income families, although Mulroney has been criticized for allowing those benefits to rise automatically as inflation has increased.