"I utterly reject any suggestion that we would leave the European Union," Xinhua news agency quoted Kenny as saying in a keynote address to the think-tank Institute of International and European Affairs in Dublin.
"The foundation of Ireland's prosperity and the bedrock of our modern society is our membership of the EU. That will not change," he said.
Kenny said the membership of the EU has brought Ireland enormous benefits and that the Irish people have consistently endorsed that membership.
He said the membership has been central to the success of Ireland's open, competitive economy, adding that Ireland's membership of the single market and the customs union are absolutely fundamental to its economic strategy.
"It gives us full access to EU trade agreements with other major markets, and a capacity to engage in global free trade that we could not possibly have on our own. It allows our people to travel, work and live freely in all member states if they choose to do so," the Irish Prime Minister said.
The EU has also been the cornerstone of much of the social progress which Ireland has experienced over the last generation, he said.
"The social dimension of the EU — respect for human rights, workers' rights, and equality — reflects a distinctly European set of values which we share here in Ireland," he said.