THERESA May has agreed with taoiseach Enda Kenny that Brexit should not lead to a "border of the past" for Northern Ireland.
The border was subject to heavy security and major disruption during the Troubles.
The prime minister said a key objective is to negotiate a free trade agreement with the EU which gives the UK the widest possible access for trading with and operating within the EU.
"The taoiseach and I, and all parties, are absolutely on the single page on this that we want to ensure that we have the best possible arrangement that does not lead to a border of the past for Northern Ireland," she said.
A study by the Irish Economic and Social Research Institute has warned that Brexit could reduce bilateral trade flows between Ireland and the UK by 20 per cent or more.
Trade between Northern Ireland and the Republic is worth around £2.2 billion per year, and the Republic continues to dominate the north's export market, accounting for about 37 per cent of the total, worth £3.6bn per year, a recent Institute of Directors report said.
Mrs May was replying to Labour leader Jeremy Corbyn as he asked if the UK will pay to access the single market post-Brexit
She said: "Access to the single market is exactly what I was talking about yesterday in my speech.
"One of the key principles, key objectives, is that we negotiate a free trade agreement with the European Union that gives us the widest possible access for trading with and operating within the European Union.
"He talks about frictionless access – this was actually a separate point, which is about frictionless borders in relation to the customs issue, a very important issue for us in relation to our relationship between Northern Ireland and the Republic of Ireland."
