Update 5.15pm: Canadian Prime Minister Justin Trudeau has spent the day meeting with the Taoiseach and President in Dublin.
Mr Trudeau discussed trade, Brexit and the gender balance in politics in a meeting with Leo Varadkar that lasted almost two hours.
An official dinner in his honour will take place in Dublin tonight.
Justin Trudeau said he has always appreciated Irish hospitality.
"For our 150th birthday, we wanted to come here to Ireland, the ancestral home of so many Irish immigrants who helped build Canada," he said.
"So many times over my life, visiting céilís or small impromptu kitchen parties I felt that famous Irish hospitality echoing down through the generations.
"And that's certainly been felt by all of us here today."
Some of the media coverage of his visit has been criticised in the Dáil chamber this afternoon, however.
People Before Profit TD Richard Boyd Barrett says too many reports have ignored a proposed trade deal with Canada - and instead focused on socks.
"Bizarrely, much of the coverage of your meeting with Prime Minister Trudeau has been focusing on the pattern of your socks and your youthfulness, when in fact this is a deal that has I would argue hugely significant and potentially very damaging consequences for our economy."
Canada and Ireland should cash in on Brexit and Donald Trump's US presidency by encouraging people and businesses to relocate, Canadian prime minister Justin Trudeau has said.
After talks with Taoiseach Leo Varadkar in Dublin, Mr Trudeau said migration should be seen as a positive.
"There are tremendous opportunities for countries like Canada and Ireland at a time where perhaps our significant allies and trading partners, in the case of the UK and US, are turning inward or at least turning in a different direction, to make the pitch that Canada and Ireland are places that are exciting and open to the world in a positive, progressive way," Mr Trudeau said.
Trade issues were high on the agenda when Mr Trudeau and Mr Varadkar met in Farmleigh House in Dublin, with the CETA agreement between the Europe Union and Canada a key focus.
The deal, which has yet to be ratified by national parliaments, took seven years to negotiate.
But it has controversial clauses, including concerns about giving companies the right to sue governments and questions about workers' rights.
Mr Varadkar said the CETA deal is progressive and not just about big business, citing its focus on environmental protections.
"I understand that there are concerns," the Taoiseach said.
"People always have concerns about free trade agreements.
"But there are many more benefits for our country and our people, our economy than there are downsides.
"It's not just an agreement for big business.
"It's also an agreement for small business, for workers and has huge potential for Ireland."
During the Canadian PM's trip, Mr Trudeau was being hosted by President Michael D Higgins at Aras an Uachtarain.
He has several other engagements in Dublin including a business lunch and a visit to see the Famine memorial statues in the city centre and a dinner hosted by the Taoiseach.
Mr Trudeau is accompanied on the trip by his wife Sophie Gregoire Trudeau and their young son Hadrien.
The visit has been arranged two months on from when Mr Varadkar's predecessor Enda Kenny met the Canadian leader in Montreal.
Mr Trudeau will leave Ireland on Wednesday for engagements in Scotland, including meeting the Queen at the Palace of Holyroodhouse on Wednesday to "honour her importance to Canada's history".
Mr Trudeau is attending the G20 summit in Hamburg later in the week.
On Brexit, Mr Varadkar said more people will want to come to Ireland as a result.
"What I anticipate, because of our economic recovery, because we are the fastest-growing economy in Europe now for two years in a row, and potentially because of Brexit, more and more people will want to come to Ireland," he said.
"We will actually have more inward migration into Ireland.
"We will be able to import the skills that we need and the knowledge that we need and the new experiences we need through a positive, open, managed migration policy."