The UK Government has denied it intends to treat Northern Ireland differently from the rest of the UK as part of any compromise to keep the Irish border open after Brexit.
Responding to an urgent question in the House of Commons following the failure to agree a conclusion to the first phase of Brexit talks, Mr Davis said it was a "falsehood" to suggest Northern Ireland was being 'left behind' in the single market.
A carefully choreographed attempt to break the deadlock in Brexit talks by agreeing a text committing the UK to allow "regulatory alignment" between Northern Ireland and the Irish Republic collapsed after it was rejected by DUP leader Arlene Foster.
A leak of the draft text prompted calls from Nicola Sturgeon for Scotland to be allowed to stay in the single market after Brexit, a demand echoed by the Welsh First Minister and London Mayor.
"I would like to take the opportunity to rebut one falsehood I saw being stirred up by various political opponents yesterday," Mr Davis told MPs.
"This was suggestion that we might depart the European Union but leave one part of the United Kingdom behind, still inside the single market and the customs union. That is, emphatically, not something the Government is considering.
"So when the the First Minister of Wales complains about it, or the First Minister of Scotland says it's a reason to start banging the tattered drum of independence, or the Mayor of London says it justifies a hard border round the M25, I say they are making a foolish mistake.
"No UK Government would allow such a thing, let alone a Conservative and Unionist one."
At a meeting of cabinet on Tuesday morning, Scottish Secretary David Mundell is understood to have reiterated comments by the Scottish Conservative leader Ruth Davidson warning that any regulatory alignment had to be on a UK-wide basis.
A Number 10 spokesman said the cabinet shared that position, adding: "That has been the Prime Minister’s view throughout."