The Canadian leader has also met the Taoiseach and President Higgins
The Canadian Prime Minister Justin Trudeau has been honoured at an official dinner in Dublin Castle as part of his two-day visit to Ireland.
We are liked minded as countries and like minded as people - Taoiseach Leo Varadkar on Ireland-Canada relations pic.twitter.com/5aSaADc64m— MerrionStreet.ie (@merrionstreet) July 4, 2017
Earlier, he and his wife Sophie met President Michael D Higgins and his wife Sabina at Áras An Uachtaráin.
Mr Trudeau signed the Visitors Book, with the message: "May we ever be united as friends and welcomed as family."
The couple also attended a reception with President Higgins.
He also met An Taoiseach Leo Varadkar for a meeting, and gave him some advice on getting women into politics.
Mr Trudeau said the issue was discussed during a 90-minute meeting between the two leaders at Farmleigh.
The two leaders even took time out to go for a jog in Dublin's Phoenix Park.
Tweeting about the run, Mr Trudeau said: "The sun came out just in time for a quick chance to see more of this beautiful part of Dublin on foot... nice pace".
While Mr Varadkar said: "After today's Dail business joined @JustinTrudeau for quick jog through #PhoenixPark."
Mr Varadkar cited Mr Trudeau as one of his political role models when he was running for the Fine Gael leadership - saying he was an example of energising the political middle ground.
The Taoiseach honoured his guest earlier with a pair of Maple Leaf socks:
Mr Trudeau's Cabinet has an equal split of men and women, while the new Taoiseach has been criticised for giving only 20% of ministerial roles to women.
Mr Trudeau said he had a helpful discussion with the Taoiseach on how to improve that.
He suggested: "For some reason, it's more difficult to get women to run for politics than it is to get men to run for politics."
In a press conference after their meeting, both leaders also addressed concerns about the CETA trade deal between Canada and the EU - with the Taoiseach arguing there are 'many more opportunities than there are downsides'.
"CETA is such a great model of a progressive trade deal," says Trudeau, says it gives citizens greater access to goods, services and jobs pic.twitter.com/Tlu9KSnWcC— Gavan Reilly (@gavreilly) July 4, 2017
Mr Trudeau also attended a business roundtable event alongside the Tánaiste and Jobs Minister Frances Fitzgerald, and visited the EPIC Ireland emigration museum in the Docklands.
Mr Trudeau will leave Ireland on Wednesday and visit Edinburgh, before attending the G20 Summit in Hamburg on Friday and Saturday.