"We have said we will meet our international obligations, but there will be our international obligations including assets and liabilities and there will be the ones that are correct in law, not just the ones the Commission want".
Pressed on reports that the eventual divorce figure could reach up to €100 billion, he said: "We will not be paying €100 billion."
He added: "We will do it (negotiate) in the meeting, we will do it properly, we will take our responsibility seriously. What we've got to do is to discuss in detail what the rights and obligations are."
The European Union's chief Brexit negotiator is expected to unveil his recommendations for the forthcoming talks with Britain.
Michel Barnier's recommendation will be based on guidelines agreed on at Saturday's summit of the 27 remaining EU member states.
European commissioners will formally adopt his recommendations this morning before he gives a press conference.
Mr Barnier has said he needs to wrap up the talks by October 2018 to get any Brexit deal through the European Parliament in time for Britain's scheduled departure from the EU on March 29, 2019.
Mr Davis said the EU could not bar Mrs May from joining Brexit discussions at future EU heads of government meetings while the UK remained a member state.
According to reports, Brussels was plotting to limit Mrs May's Brexit discussions to direct meetings with Mr Barnier.
Such a move would run contrary to Mrs May's claim that she would be negotiating directly on the terms of Brexit with fellow European leaders.
Mr Davis said: "The decisions in this exercise at the end of the day are taken in Council - that's a gathering of all the leaders of the European Union - and, frankly, until the day we leave, we are full members of the Union, we have every right to attend every Council and we will exercise our right.
"Just as we are obeying the laws of the Union, exactly to the letter, we are also going to expect our rights.
"The idea that somehow one side of the negotiation can dictate how the other side runs a negotiation is laughable.
"This is an exercise in trying to shape public opinion and trying to pressurise us - it won't work."
Meanwhile, Fianna Fáil's Brexit spokesperson said reports that the UK could be facing a Brexit bill of up to €100bn, could place Ireland in a "difficult position" which would be "extremely damaging" to Irish jobs, Irish agriculture, tourism and retail sectors.
Speaking on RTÉ's Morning Ireland, Stephen Donnelly said "the danger is the UK Government and Prime Minister May ends up in a corner from which it's very difficult to move".
He also said the Government's Brexit plan lacks political vision and ambition.
Mr Donnelly said the strategy, released yesterday, is a "good introduction to Brexit" but what we needed was a plan.
He said there should be a detailed, costed, timetabled plan to detail how the Government will interact with farmers, tourism and people working in the UK but instead the report talks about "response plans that will be developed in time".
Mr Donnelly said this was "not good enough".
He described the outcome of last Saturday's meeting of the EU council as a re-statement of existing agreements.
Mr Donnelly also told RTÉ News that reports the UK could be facing a bill of €100bn could place Ireland in a "difficult position."
The Wicklow TD said it could be "extremely damaging" to Irish jobs, as well as the agriculture, tourism and retail sectors.