He said it is not for the British government to decide what happens on the Irish side of the border.
The minister also said similar advice applies to those trading between the UK and France.
Mr Lidington met business leaders in Derry on Friday over Brexit.
Mr Lidington also held talks with community groups in the city about relations on the ground.
“It can’t be for UK ministers to determine or give authority upon what steps are taken in the Irish government anymore than what we can say the French would be doing at Calais,” he said.
“That is something the French authorities would have to take their decision on.
“The Belgians would have to take the decision on what happens at the Port of Ostend.
“We can only describe, as we did yesterday, what we can do within the powers that we as a UK government have.”
He added the government will be doing all it can to avoid a hard border.
“Our message to business trading across the border is that our commitment is to respecting every detail of the Good Friday and Belfast Agreements and working as hard as we can to ensure there is no friction on the border.
“We will be striving to keep the border open but what I can’t do is say what the Irish government would do within its jurisdiction as they will have to talk to the European Commission.”
The minister also said the timing of a letter from the chancellor yesterday, warning of the economic impact of a no-deal Brexit, was a “coincidence”.
Philip Hammond has been criticised for publishing the comments just hours after the government had sought to provide reassurance with guidance on a no-deal scenario.
But Mr Lidington dismissed any idea of a “conspiracy”.
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