Last year, 300,000 pupils sat for the primary leaving exam, but only 40 per cent will be able to join secondary schools this year owing to lack of space.
"We intend to change this in the next three years," the president said. "The government will build a secondary school in each of the country's 920 sub-counties." Each sub-county has 10 to 20 primary schools.
In a departure from the past, the new institutions will be day rather than boarding schools. "I don't want boarding schools because they are the cause of the high cost of secondary education in Uganda," said President Museveni, who is currently campaigning for the presidential election to be held on March 6.
The universal education programme is behind schedule as the government seeks more cash.
Construction of the new schools will not be easy for a government that is still struggling to provide basic facilities for children enlisted under a national drive to offer primary places to four youngsters from every family.
Enrolment in primary schools rose from 2.5 million in 1997 to 6.8 million this year. But the rush has hit the quality of education on offer. And delays have hit the pla to build 9,000 new classrooms in primary schools and complete 4,000 others in 18 months at a cost of pound;35 billion Ugandan shillings (pound;13m).
Nevertheless, Uganda is held up as a model example by donor countries of what can be achieved.
These countries are due to meet at the end of the month to discuss funding for plans to achieve universal primary education across the world by 2015.
Many pupils continue to take lessons in makeshift classrooms while the government urgently needs cash to buy desks, textbooks and other learning materials. It has been unable to provide textbooks on the core subjects to schools.
The added costs of the new secondary schools and more teachers - secondary teachers earn pound;30-pound;50 a month compared with pound;28-pound;30 for primary teachers - is likely to eat into the budget earmarked to increase access to primary education.
The number of primary teachers has risen from 85,000 to 110,000, including 15,000 untrained staff, partly thanks to international debt relief.
But there is general concern in Uganda that unless more children are able to transfer from primary to secondary school, fewer parents will be prepared to enrol their children. For this reason, expansion of secondary education has become a key issue in the presidential campaign.
Global campaign for education: www.campaignforeducation.org