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Prime Minister Theresa May yesterday held a press conference with the Irish Taoiseach Leo Varadkar after talks at 10 Downing Street:

Prime Minister Theresa May

I would like to extend a warm welcome to Leo Varadkar to Downing Street today for the first time and offer my congratulations on his appointment as Taoiseach and leader of Fine Gael.

The unique relationship shared between the United Kingdom and Ireland is one of friendship, close cooperation and a deep sense of shared endeavour, bound by common values and generations of family links between our people.

The Taoiseach has said he believes in an Ireland where every person has an opportunity to succeed and share in prosperity. And I share a similar belief that the United Kingdom should be a place where everyone should have the chance to live a secure and happy life - a country that works for everyone, not just the privileged few.

We also spoke about the unimaginable tragedy which struck Grenfell Tower last week. The government will continue to do absolutely everything possible to help all of those affected through the difficult days, weeks, months and years ahead.

We spoke too about the appalling attack on Londoners in Finsbury in the early hours of this morning. As I said earlier, this was an attack that once again targeted the ordinary and the innocent going about their daily lives. Our thoughts and prayers are with the family and friends of the man who died and those who were injured.

The Taoiseach expressed his deepest sympathies for those affected by these horrific events and we both agreed that this kind of hatred and evil that leads to terrorism would never prevail.

Last week, the Taoiseach and I spoke and we agreed on the crucial need for the parties in Northern Ireland to form a fully functioning Executive by the 29 June deadline and how we would continue to engage closely on this important issue and reaffirmed that today.

We have both met the two main parties to make clear that the UK and Ireland would do everything we can to work with them and the importance of reaching an agreement by 29 June.

It is my firm belief that with good will on both sides a resolution can be reached which builds on the progress made in the last round of discussions.

And my government remains absolutely committed to a successful outcome from these talks and we remain steadfast in our support for the Belfast Agreement and its successors.

As the United Kingdom embarks on leaving the European Union, I fully respect that Ireland will remain an EU member state and that’s why it is more important than ever that the relationship between our countries continues to go from strength to strength.

We are leaving the European Union, but we are not leaving Europe – and we want to remain committed partners and allies of Ireland and all our friends across the continent.

Trade between our countries is worth over £43 billion a year and supports 400,000 jobs. And there are also complex supply chains that benefit both our countries. And as I’ve said before, no one wants to see this diminished.

I am personally committed to ensuring a practical solution that recognises the unique economic, social, cultural and political context of the land border with Ireland - which so many people pass through everyday and it remain our priority to work closely with the Irish government to ensure a frictionless and seamless a border as possible.

And I made this clear in my letter to Donald Tusk triggering Article 50 and that we want to maintain the Common Travel Area between us to make sure the UK’s withdrawal from the EU does not harm the Republic of Ireland.

We also want the reciprocal rights that our citizens enjoy in both countries to continue, including the rights guaranteed under the Belfast Agreement.

And both we and the EU have made clear that we want to resolve this as a matter of priority and I am pleased that as negotiations begin in Brussels today we can start working in earnest together on joint solutions.

And it is with this shared sense of purpose that I believe our 2 countries can build even deeper ties and our unique relationship will become even closer and stronger.

The Taoiseach and I have had constructive discussions today. I look forward to working with him and to continuing the close relationship that our 2 countries have enjoyed for many more generations to come.