Speaking at Trinity College Dublin during a two-day visit to Ireland, Carney said the world was experiencing a "global rupture", with economic ties being "weaponised" and conflicts becoming more complex.
"Canada, Ireland and Europe are increasingly and immediately vulnerable to once-distant threats," he said.
However, he said both countries were well placed to respond by working together and strengthening ties with "reliable partners" that share democratic values.
Earlier, Carney met Taoiseach Micheál Martin at airport.
"I know I speak for the people of Mayo, and indeed for the Irish people more broadly, when I say that we are deeply honoured to welcome him back," the Taoiseach said.
Carney, whose grandparents emigrated from Co Mayo to Canada, replied: "Micheál, thank you for welcoming me back home."
"It is a true pleasure to return to Dublin, and an honour to be the first Canadian prime minister in a decade to be making an official visit here."
The visit comes as Canada looks to strengthen relationships with partners beyond the United States and as Ireland seeks to expand international trade links.
At a joint press conference, Carney also expressed confidence in an Irish investigation into exports of alumina that ultimately reached Russia.
"I have every confidence in it," he said, adding that Ireland and the European Union had been "at the forefront of supporting Ukraine".
Martin said Ireland gives no support to Russia's war effort and would consider any further action once the investigation is complete.
Asked about his Irish roots, Carney said they continue to shape his outlook.
"Drawing on that strength and that heritage is necessary," he said, adding that international relationships work best when "sovereignty is respected".
The prime minister will travel to Co Mayo on Sunday to visit Aughagower, where his grandparents were born, attend Mass and visit family graves before meeting President Catherine Connolly in Westport.
The trip is the first official visit to Ireland by a Canadian prime minister since 2017 and the first ever official visit by a Canadian prime minister to Co Mayo.
