Some 15,000 trees sponsored by Coillte, will be distributed to community groups by local authorities all over the country.
Events planned to mark National Tree Week include forest walks, tree planting ceremonies, workshops, talks and competitions.
Agriculture Minister Brendan Smith marked the week with tree planting ceremonies at schools in Co Cavan.
He congratulated the Tree Council of Ireland on organising so many varied and interesting events and activities.
Mr Smith urged people to attend such events and to avail of the opportunity to appreciate trees and their many benefits.
“A specific week designated as National Tree Week gives us the opportunity to raise awareness about trees and their many benefits,” he said.
Mr Smith said even though they are a major part of the landscape, the significance of trees can sometimes be underestimated.
“National Tree Week provides us with an invaluable opportunity to appreciate the value of trees and the importance of planting more trees so that future generations may also enjoy those benefits,” he said.
Mr Smith noted, in particular, the contribution forestry makes by way of employment, climate change mitigation and enhancement of biodiversity.