The Philippine Supreme Court on Tuesday upheld most of a controversial reproductive-health law, handing the government a victory in its effort to provide greater public access to birth control and family-planning education in the heavily Catholic country.

The implementation of the law has been held up for more than a year by a legal challenge from the Roman Catholic Church and faith-based groups. Advocates of the law say it will help slow the country's population growth of more than 2% annually by providing people more access...