Across the country, more than 500,000 children have enrolled in school. Mr Nkurunziza, the former leader of a rebel group, was elected this year and abolished school fees after he was sworn in last month.
Free primary education is one of the United Nations' Millennium Development Goals. The UN estimates that countries need to spend $9bn (£5bn) to provide free primary education for all the world's children by 2015. Currently 115 million children are thought to not attend school.
Several countries in sub-Saharan Africa, including Ghana, Tanzania and Kenya, have scrapped school fees in recent years, whichcaused a dramatic rise in attendance. In Kenya, enrolment increased by 88 per cent.
Most families in rural areas cannot pay the £2 a term it cost to send a child to school, and the abolition of fees has been welcomed by parents and international groups. But head teachers complain that they have not been given extra resources to deal with the rise in pupils. In Burundi, more than 150 children crowded into one classroom, and in Ghana, some pupils have been turned away because their nearest schools simply have no room for them.
Meanwhile, the world's oldest primary school pupil, Kimani Nganga Maruge, an 85-year-old Mau Mau veteran, travelled to New York from Kenya to draw attention to the opportunities and problems presented by free education. The great-grandfather enrolled in his local primary school last year after fees were scrapped, and is learning to read and write English and Swahili.
He said: "I never went to school when the British were in charge, but I am very happy that I now have the chance to learn to read the Bible.
"Someone told me I may get some compensation money from the British because I fought with the Mau Mau, and I want to learn maths so I can count my money."
His head teacher, Jane Obinchu, has accepted all pupils who want to learn at her school, but said her staff were struggling to cope with the workload. More than 70 children are crammed into each classroom - many sit on the floor because there are not enough desks - and teachers often end up teaching several subjects at once.
"There are children here who are eager to learn and I want to give them every chance to study, but we have not been given any extra teachers or funds. The brightest children are fine, but the slowest ones end up being forgotten in the huge classrooms we have."
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