Mr Davis insisted progress was being made and claimed any delays in the talks were down to Brussels attempting to secure a bigger financial settlement from the UK.
European leaders will begin a two-day summit on Thursday which will include debate over whether the Brexit talks should progress to the subject of future trading relations.
Chief negotiator Michel Barnier has demanded progress is made on the EU’s priorities before trade is discussed.
Mr Davis told MPs discussions on those areas, including the future of Irish border arrangements, were moving forward but could not be concluded until the trading relationship between the UK and the EU had been agreed.
“We all must recognise that we are reaching the limits of what we can achieve without considering our future relationship,” Mr Davis said.
He repeatedly came under-fire from opposition MPs over the failure of the talks to move on to trade But Mr Davis maintained it was the EU dragging its feet.
“They’re using time pressure to see if they can get more money out of us, and bluntly, that’s what’s going on,” he said.
Mr Barnier and other European officials have repeatedly suggested leaders of the other 27 nationals will be recommended not to press ahead with trade talks at this week’s summit.
But following Theresa May’s unexpected trip to Brussels on Monday, Mr Davis hinted Mr Barnier may be more positive than expected.
Mr Davis said he hoped his European counterpart “will argue for more progress both on transition and on the future relationship, but it is for him to make that persuasive case on the day”.
Pressed on the risk of leaving the EU without a trade deal, Mr Davis said the Government was “straining every sinew” to secure an agreement but ministers “have to have the right to walk away”.
Home Secretary Amber Rudd struck a different tone on the possibility of hard Brexit, telling the Home Affairs Selection Committee: “I think it is unthinkable that there would be no deal.
“It is so much in their interest as well as in ours; in their communities’, in their families’, in their tourists’ interests to have something in place.”