"The group would deal with the specific challenges arising from the new European Union cyber legislation, Brexit and work with governments in order to protect businesses in Ireland and the UK", Dwyer said.
The European Commission has today set out its principles for the political dialogue on Ireland and Northern Ireland in the Brexit negotiations.
This echoes the view of the Prime Minister of the Republic of Ireland, Leo Varadkar, who said this July that his government is not willing to help design a Brexit border, as that is the UK's responsibility.
The Foreign Secretary insisted it was not "beyond the wit of man" to find solutions for problems such as the future of the Irish border.
The Commission's chief Brexit negotiator also made clear that the Common Travel Area regime between the United Kingdom and Ireland can not be negotiated before there is "sufficient progress" on citizens' rights and the financial settlement.
"We welcome the Government's commitment to negotiating an interim period so that firms can ensure they are ready to adapt to the changing relationships and thrive under the new partnership being created with the EU".
London, Dublin and Brussels all agree that the maintenance of an open border, without checks or CCTV cameras, is essential under the Good Friday Agreement.
The UK has argued that especially the Ireland question can not be disentangled from other issues, such as customs and future trade deals, and therefore these negotiations should run in parallel.
Non-Profit Calls for UK-Ireland Cyber Task Force
"All this could be avoided if the British government took the sensible decision, on leaving the EU, to remain in the single market or at least the customs union".
The future of the border is critical as once Britain leaves the European Union (EU) it will be the only land border between the United Kingdom and the bloc.
The British government has voiced frustration at the refusal of European Union negotiators to open discussions on a future free trade pact until London makes concessions on elements that must be settled to avoid legal chaos when Britain leaves in March 2019.
"I think we can all work together to come up with a solution to that one", he said.
Its chief negotiator, Michel Barnier, acknowledged that a unique solution would need to be found to the border issue, but said he was "worried" by the British proposals.
Northern Ireland's border with the Republic of Ireland will be the only land frontier between the European Union and Britain once the country withdraws, expected to happen in March 2019.
The UK government has ruled out a suggestion of joint authority in Northern Ireland, should talks aimed at restoring the Stormont Executive fail.
The EU wants commitments around peace funding.