DUP leader Arlene Foster said Theresa May's speech has "set forward the basis upon which it would be possible to move forward".
Ms Foster welcomed that Ms May said “she will not countenance any new border being created in the Irish Sea between Northern Ireland and the rest of the United Kingdom”.
She also warned that securing a “sensible outcome for everyone will require the EU27 to consider innovative solutions rather than rule out any proposal which has not been conceived in Brussels”.
Ms Foster said she believes the British government’s proposals from August 2017 “did not receive a fair hearing in many quarters”.
DUP deputy leader and Westminster leader Nigel Dodds also said Ms May had set out the way to avoid a hard border in the August 2017 British government position paper and again on Friday.
He wrote on Twitter: "Theresa May says that she "is not going to allow anything that would damage the integrity of our precious Union". Excellent."
He added: “PM sets out the sensible approach of how no hard border can work. As she (and we) have been saying all along. It’s in the papers the Govt produced last August.”
SDLP Leader Colum Eastwood was not so upbeat.
Mr Eastwood said people across Britain and Ireland were looking for answers and Theresa May “failed that test”.
“We have now had 3 keynote speeches from Theresa May on Brexit – none of them has offered any solutions to the border question in Ireland,” he said.
“The Prime Minister’s commitment to work for a solution on the border is a belated recognition of reality, however that commitment is severely undermined in the same speech when she advocated the very same customs proposals which were widely and comprehensively dismissed last year.
“To save her the bother of searching, the SDLP is happy to restate the only solution that makes any sense.
“Northern Ireland should remain in the single market and the customs union to avoid a hard border in Ireland. To avoid a border in the Irish Sea, the island of Britain should remain in the customs union and the single market.”