The European Union on Monday warned Britain time was running out to seal a Brexit deal this autumn and ensure London does not crash out of the bloc next March adding to pressure on Prime Minister Theresa May.
He told BBC Two's Newsnight: "The uncertainty around Brexit and the border is a concern, certainly from a policing perspective".
He said June's European Union summit was a "key rendezvous" to reach a deal that can be ratified before the United Kingdom leaves.
The backstop, a fallback position or guarantee that there will be no infrastructure on the Border and commitment by the United Kingdom to maintaining North-South regulatory alignment, is part of the proposed Withdrawal Agreement that is supposed to be finalised by October. A political stand-off has ensued over the vexed issue.
"Michel Barnier has made it very clear, and I agree with him, that there will be no withdrawal treaty if there isn't a backstop dealing with the Irish border in that treaty", he said.
"I think nobody must underestimate the key rendezvous of June", France's Barnier told a security conference in Brussels.
The Irish government is hopeful a comprehensive resolution could lie in the concept of shared customs territory.
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Under a customs partnership, the United Kingdom would collect tariffs for Brussels.
However, the United Kingdom cabinet is at odds on the issue. The alternative model being considered by the Cabinet is known as maximum facilitation, or "Max Fac", which would rely on new technology and trusted trader schemes. Some key issues related to the withdrawal agreement need to be settled, Reuters quoted her as saying. "In June we need to see substantive progress on Ireland, on governance and all remaining separation issues", Zakharieva said.
Mr Jones said his government had "pushed the UK government to be more transparent and open in its talks with other countries" but they had "not been invited to take part in working groups that have been set-up, for example the Australia-UK working group".
He added he "cannot for a moment believe" the Irish government will put administrative systems in place which are not introduced by the UK.
Shadow transport secretary Andy McDonald said there was an increasing frustration and anger among the freight and logistics industry at the Government's "cavalier it'll be alright on the night" approach.
But the United Kingdom government has ruled out establishing a customs union with the EU.