The Prime Minister has said any deal with the EU over Brexit "must protect the union" between Northern Ireland and Great Britain.
Theresa May, writing in the Sunday Times, also said there could be no hard border in Ireland.
"As a proud unionist and prime minister of the whole United Kingdom I am clear that any deal with the EU must protect our precious Union and also honour the agreements that were reached in the historic Northern Irish peace process," she said.
"This means there can be no hard border between Northern Ireland and Ireland, or between Northern Ireland and the rest of the UK.
"We will uphold the Belfast agreement in full - and we will ensure the constitutional and economic integrity of the whole United Kingdom."
Mrs May added that any agreement "must create as little friction as possible" for trade both within the UK and with Ireland.
Her comments came after Cabinet divisions broke into the open after proposals for a customs arrangement with the EU were branded "crazy" by Foreign Secretary Boris Johnson.
"You can trust me to deliver. I will not let you down," Mrs May wrote.
The PM stressed the UK would be aligned with Brussels on some issues as there had to be "compromises" after withdrawal.
The PM said: "So, Brexit means that, while we may sometimes choose to take the same approach as the EU, our laws will be made in Westminster, Cardiff, Edinburgh and Belfast, with those laws tried by British judges."
Mrs May has divided the Cabinet into two groups to consider the customs options being looked into.
The customs arrangement with the EU that Mr Johnson opposes would see the UK collecting tariffs on behalf of Brussels.
An alternative option called maximum facilitation, known as "Max Fac", would rely on new technology and trusted trader schemes to get trade to flow smoothly with the EU after Brexit. However, Sinn Fein MLA Mairtin O Muilleoir hit out at Mrs May's article, describing it as "devoid of detail and free of facts".
"Theresa May could have written the same article any time over the last 23 months," he said.
"The British Tory party's proposals for a red, white and blue Brexit disregard the vote of the majority of people in the north to remain in the European Union," he said.
"Two years after the referendum and six months away from the conclusion of negotiations Theresa May has no plan or agreed approach to the British Brexit problem."
Mr O Muilleoir said the solution to the Irish border problem was "clear".
"The British Government must respect the vote of the people of the north and provide for the north to remain within the EU single market and customs union," he said. "It must protect the Good Friday Agreement and retain access for citizens to the European Court of Justice and the Charter of Fundamental Rights of the European Union."