It was his first visit since the coronavirus pandemic struck and there have been calls for closer collaboration between Ireland and Britain to tackle the threat.
"I can not overstate how important the close co-operation that we have seen between central and devolved government will continue to be to this", he added.
Boris Johnson had earlier exchanged pleasantries with first and deputy first ministers Arlene Foster and Michelle O'Neill on the veranda in the castle gardens.
British Prime Minister Boris Johnson and Taoiseach Micheál Martin have met for the first time since the Fianna Fáil leader was elected to the position in June.
"Together, we will make sure Northern Ireland is ready to take full advantage of the many opportunities that lie ahead and that no part of Northern Ireland is left behind".
Covid-19 is expected to top the meeting's agenda, as yesterday saw confirmation that the United Kingdom, the Republic's nearest trading partner, had officially slipped into a recession.
Asked how Wilfred was getting on as the posed for the cameras at Hillsborough Castle, Mr Johnson enthused: 'He is getting to the stage where he is starting to vocalise when he wants us'.
The ongoing fight against coronavirus, the Irish-British relationship and an economic recovery plan are also expected to be on the agenda.
The United Kingdom, which formally left the European Union on January 31, is seeking to negotiate a new free trade accord by the end of the year, when a transition period that maintains the main economic terms of its membership will expire.
The meeting is due to round off with a focus on bilateral relations between Dublin and London, with a press conference later in the afternoon.
Johnson announced plans to establish two new bodies to work with his government on marking the centenary next year of the creation of Northern Ireland.
The Northern Ireland Executive will receive €2.2 billion additional funding this year for its Covid-19 response.
The Taoiseach said he has never been an advocate for partition but said people can learned from the centenary commemorations of Northern Ireland.
Northern Ireland Secretary Brandon Lewis also welcomed the first stage of the government's centenary plans.
He added: "The establishment of a Centenary Forum and Centenary Historical Advisory Panel will offer us the opportunity to work with a broad spectrum of people from across the political parties, business, tourism and the voluntary and community sectors".