He said he was confident the EU would not bring Ireland back to the “borders of division” after Brexit is triggered.
Speaking at the Mansion House before the Institute of International and European Affairs, Mr Kenny said a 10-year plan would help protect Ireland.
“As a direct response to Brexit, I have asked the Ministers for Finance and Public Expenditure and Reform to prepare an ambitious multi-annual 10-year capital plan that will make Ireland a far better place in which to live and work,” he said.
“That plan will make prudent and effective use of our own resources, as well as resources available to Ireland as a member of the European Union.
“We are already in active discussions with the European Investment Bank, which recently opened an office here in Dublin. I am confident those discussions will lead to significant further EIB investments in Ireland.
“That new plan will show how we will invest in roads, in public transport, in energy, in water, in schools, in higher education, and in hospitals and health facilities.”
Mr Kenny said Ireland must remain “at the heart of Europe” as the Government prepares to plan for Brexit.
He admitted that Britain’s exit from the EU is a “serious direct threat to Ireland’s economic prosperity.”
Setting out part of Ireland’s position in advance of Brexit likely being triggered next month, Mr Kenny said Ireland would need to protect the “hard-won peace” on the island.
He said common values in the EU were under threat and must be defended.
“We must remain at the heart of Europe and open to the world. We must protect the hard-won peace on our island, and we must pursue thoughtful, prudent, but ambitious economic policies,” he said.
The Government’s plan for Brexit combines these three essential elements, and key challenges lie ahead, said Mr Kenny. “So for Ireland to succeed and prosper, we must remain at the heart of Europe and we must preserve the hard-won peace on our Ireland. The final, and enormous, challenge is to protect and grow our economy.
“Brexit is a serious, direct threat to Ireland’s economic prosperity. The potential impacts are profound, right across the economy. Key sectors, such as agri-food and fishing, face particular risks and challenges.
“These sectors are among Ireland’s priorities as the agri-food sector has traditionally been reliant on the UK export market, while fishing depends enormously on access to the waters around Britain.”
In the Dáil during a debate on Brexit, Sinn Féin leader Gerry Adams said a “hard border” would undermine the Good Friday agreement.
During a debate, Foreign Affairs Minister Charlie Flanagan said: “There will be a need for the British government to definitively factor into their own negotiating position with the European Union in the stated objective in relation to the border. I reinforced this message in my meeting with the secretary of state for Northern Ireland James Brokenshire in our meeting yesterday.”