The EU's Brexit guidelines state that Irish border issues should be tackled before talks on a trade deal can begin.
Mr Davis said it was "wholly illogical" to think that the border issues can be separated from a trade deal.
He was speaking on ITV's Peston on Sunday.
Mr Davis said that the phasing of the negotiations would now be "the row of the summer".
The Brexit Secretary said that the UK is seeking a "very ambitious" trade deal with the EU, alongside a customs arrangement.
He said: "How on earth do you resolve the issue of the border unless you know what the customs agreement is, what the free trade agreement is, whether you need to charge tariffs at the border?"
Sinn FÃ©in president Gerry Adams said that Mr Davis's remarks are "a direct challenge to the Irish government and to the negotiating stance that was outlined by Michel Barnier when he visited Dublin last week".
Mr Barnier, the EU's chief negotiator, reiterated the EU's preferred phasing in a speech to the Irish parliament, saying that "sufficient progress" must be made on the preliminary issues before moving onto a trade deal.
Mr Adams said Mr Davis's remarks "emphasise the need for the Irish government to urgently press the European Council to secure for the north special designated status within the EU".
Speaking in the Republic of Ireland on Friday, Tony Blair warned that a hard border on the island would be a "disaster".
The former UK prime minister told a meeting of MEPs in County Wicklow he believed there was a "common desire" to make Northern Ireland a "special case" in Brexit talks.
The UK and Irish governments have both said they do not want a return to customs posts on the border after the UK leave the EU.
The EU's negotiating guidelines call for a "flexible and creative" approach to the customs issue.
Mr Barnier visited a food export business in County Monaghan on Friday, saying that he wanted to "work with all these people on the ground to find solutions" to the border question.
He described the forthcoming Brexit talks as "extraordinary and very complex and difficult".
"This negotiation will not only be financial, legal or technical - in my view, it will first [be] human and social and economic," said the French politician.
On Thursday, Mr Barnier said the Irish border issue would be one of his three priorities in the negotiations, adding that he would work to avoid a hard border.
But he emphasised that there would have to be some form of customs controls as a result of Brexit.
The Brexit Secretary David Davis has said he does not accept that Irish border issues can be resolved in the first stage of the UK negotiation with the EU.