Welsh Assembly Members are to vote on whether they think the process to invoke Article 50 should go ahead.
The move comes after the Supreme Court ruled that the Welsh Assembly does not have a legal right to be consulted by UK ministers.
But, speaking on The Wales Report, Mr Jones said he would tell colleagues they cannot block the process when they vote in the Senedd in Cardiff and that Westminster should take note.
Carwyn Jones said UK must listen to Wales
There will be a vote in the assembly on Article 50
Discussing the ruling, he said: “I think the key words were we are not legally compelled to be consulted. But constitutional we are.
“To be absolutely clear, there will be a vote in the assembly on Article 50. It’s important members are able to express their views.”
Responding to interviewer Huw Edwards who raised the point Westminster was not obligated to listen to the Welsh vote, whichever way it went, Mr Jones warned against it being dismissed.
Theresa May with Carwyn Jones outside the Senedd
He said: “The UK is in a precarious position. One of the issues I’ve warned against is as the UK leaves the EU, that doesn’t lead to the UK itself collapsing.
“I’s hugely important that the process and the deal itself has the widest possible support across the UK, so ignoring the celtic nations to me is a recipe for disunity in the years to come.
“Personally, we have to obviously take account of the way people voted in Wales and I certainly don’t want to delay what is going to happen, which is that the UK will leave the EU.
Government Loses Brexit Vote Appeal
Tue, January 24, 2017
Britain's most senior judges ruled that Prime Minister Theresa May does not have the power to trigger the formal process Article 50 for the UK's exit from the European Union without Parliament having a say.
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Issued by the Supreme Court of (top row, from the left) Lord Neuberger, Lord Mance, Lord Kerr, Lord Sumption, (bottom row, from the left) Lady Hale, Lord Clarke, Lord Wilson and Lord Hodge, who agreed with the majority decision that the Government could not trigger Article 50 without Parliamentary approval.
“But it’s hugely important that the process is done in such a way that is least harmful to Wales and to Britain.”
Mr Jones said he was “disappointed” with the Supreme Court ruling. He added there was a role for Wales, Scotland and Northern Ireland to play on certain issues where there was no UK banner, such as with farming and fisheries.
Asked what Mr Jones would be saying to his colleagues on which way to vote on the triggering of Article 50, he said he was not standing in the way of Brexit and it was Leavers who were wasting time debating otherwise.
He said: “I’ll be saying we can’t block the Article 50 process, we can’t look to overturn the referendum result, that result has to be respected, there’s no going back from that.
“We have to move the debate on. We produced a white paper this week, it gave ideas as to what the way forward should be.
“Now the response we have to that sometimes is ‘oh, you’re re-fighting the referendum campaign’. We’re not. It’s the leavers who keep on re-fighting the referendum campaign. That’s done that’s dusted, we move on from that now.
“The debate now is about how we leave, not if we leave and that is a debate that has enormous consequences if it’s got wrong.
“If it’s got right, actually I think this is manageable, but if it’s messed up the consequence for the Welsh economy for many many years will be disastrous.”
Carwyn Jones said colleagues would not vote against Article 50
The Supreme Court judgement means Theresa May cannot begin talks with the European Union until MPs and peers give their backing. But this is expected to happen in time for the Prime Minister’s March 31 deadline.
Mr Jones and Plaid Cymru leader Leanne Wood were accused of trying to sabotage Brexit after they unveiled a 64-page paper calling for the UK to remain in the EU’s Single Market and to continue the bloc’s freedom of movement rules.