Enda Kenny has arrived in the UK for a two-day visit saying it was important for the European Union to include a strong Britain.
The Taoiseach will meet British PM David Cameron before moving on the United States later in the week for talks with president Barack Obama.
Speaking during a visit to Manchester, Mr Kenny said he will discussing a range of issues with Mr Cameron including visa flexibility, trade and Northern Ireland.
He said: " And we want to talk about the question that Britain must answer for itself in the context of its place in Europe and for the future.
"From our point of view, clearly we have very close relations with Great Britain and that's going to continue at the very highest level.
"But also we have clearly indicated our view of the future from an Irish point of view of being with the eurozone and with the euro and with the 500 million market that's there.
"So we take the view that it's very important that the European Union has a strong Britain as part of that. It's strong for British business, it's strong for Irish business as a consequences and we have the potential of dealing with a market of 500 million people.
"These are matters that should not be treated lightly, that people have to involve themselves in the serious debate about the future because it affects everybody, particularly the children who are going to come behind us."
Opening phase one of the Irish World Heritage Centre, in Manchester, he told his audience that "our country's come through a very difficult period in the last three years" but added that " I'm glad to say that the reputation of Ireland and the integrity of Ireland and the name of Ireland has been restored internationally."
Asked later if he had a message to the Irish people in Manchester, he said: "We've come a long way in a short time.
"We've made good progress because of the patience of the people and the way in that they have accepted the enormous economic challenges.
"We still have a distance to go but our good name has been restored. Investment into the country is very strong. The Government for this year are focusing on jobs, on continuing to restructure the banks, on dealing with small and medium enterprises and on the provision of continued reform to meet our targets. That's very important.
"So we're not going to lose any momentum, you can to tell the Irish people that in Manchester."
Earlier, the Taoiseach deligh ted well-wishers looking for the obligatory selfie picture as he started his visit in the city centre.
Mr Kenny was persuaded to pose by County Mayo-born barman Fabian Bohan-taghian who whipped out his phone as he served the smiling premier with a coffee.
The PM was sampling the delights of an Irish coffee bar outside the front of Manchester Town Hall, but refused a tot of whiskey. He managed a thumbs-up gesture and smile for Mr Bohan-taghian and his colleagues who crammed into the shot.
Later, at the new Irish World Heritage Centre, he toured the building, including a shop devoted to Irish products.
He talked about the crisis in Ukraine reminding those gathered in the foyer to listen to his speech how 30,000 Irish soldiers died in the Crimean War in the 1850s.
And Mr Kenny talked about the "extraordinary impact" of the visit of The Queen to Ireland two years ago saying: " When she was leaving at Cork Airport, Her Majesty said to me 'of all of these state visits that I've ever done in 60 years this is the one that I really wanted to do'."