The UK is already challenging Brussels over its Brexit divorce bill plans, David Davis has said as he laughed off concerns about Boris Johnson's controversial suggestion the EU could "go whistle" if it makes "extortionate" demands.
Labour leader Jeremy Corbyn accused the Foreign Secretary of arrogance and peers raised worries over how his comments will be received in the rest of the bloc.
European Commission president Jean-Claude Juncker has suggested that the bill, which covers outstanding liabilities for programmes which the UK signed up to as an EU member, as well as ongoing costs including staff pensions, could be around £50 billion, while unconfirmed reports have claimed it could reach almost twice that figure.
Mr Davis said the British strategy on the divorce bill was "not to pay more than we need to" and will not accept the EU's "first claim" without going through it line by line.
"There will be a process of challenge going on here and that will happen and has started already in the negotiated process to establish whether or not we believe in that particular case they have made a legally defensible argument or not," he said.
Asked about Mr Johnson's comments, the Brexit Secretary laughed before telling peers: "Bluntly, I wouldn't worry. I mean you will have to get the Foreign Secretary here to explain his views if you really wanted to. I'm not going to comment on other ministers."
Mr Davis told the European Union select committee that all of British newspapers are read in Brussels and they "take them, if anything, too seriously".
"More importantly in the context of the 27, actually very little of what happens here percolates across."
The Foreign Secretary was responding in the House of Commons to questions over the proposed "divorce bill" which the UK is expected to receive next week as Brexit negotiations resume in Brussels.
Addressing Mr Johnson at foreign affairs questions in the Commons, Tory eurosceptic Philip Hollobone said the UK had made a net contribution of £209 billion to the EU since joining in 1973, adding: "Will you make it clear to the EU that if they want a penny piece more then they can go whistle?"
Mr Johnson replied: "I'm sure that your words will have broken like a thunderclap over Brussels and they will pay attention to what you have said.
"He makes a very valid point and I think that the sums that I have seen that they propose to demand from this country seem to me to be extortionate and I think 'to go whistle' is an entirely appropriate expression."
Speaking outside the Commons chamber, Mr Corbyn said: "I think it is ridiculous for the Foreign Secretary to approach important and serious negotiations with that silly, arrogant language that he so often employs.
"Treat people with respect and there's a fair chance you will be treated with respect in return.
"If you start on the basis of those silly remarks, what kind of response does he expect to get?"
Mr Corbyn is due to meet the EU's chief Brexit negotiator Michel Barnier in Brussels on Thursday, to set out his party's approach to Brexit and hold "exploratory discussions" about the negotiations ahead.
He said Labour would "pay what we are legally required to pay", but nothing beyond that.
"We have to negotiate intelligently and sensibly, but above all negotiate with respect and expect to be respected in return," said Mr Corbyn.
The UK's negotiating team under Mr Davis is due to begin the first full round of negotiations with Mr Barnier on Monday.
Mr Johnson's comments came after Number 10 sources played down suggestions that Theresa May plans to walk out of Brexit talks in September to show defiance over EU demands for a divorce bill worth tens of billions of pounds.
The Foreign Secretary said the public wanted the Government to "get on and deliver a great Brexit" and insisted that "there is no plan for no deal because we are going to get a great deal".
Mr Davis said Mr Barnier wants to recommend that parallel negotiations on the exit settlement and future trading arrangements begin in October or November.
The negotiator is a principled man who is "very French, very logical, tough but not wholly inflexible", he added.
Settling future rights for citizens is an "issue of civilisation", he said.
"I don't expect we are going to get to a treaty in the immediate future, but what I would hope we would get to is a very substantive heads of agreement which we can initial and say that's what we want at the end game," he added.
"That I think will give people a degree of confidence in their own lives."
Mr Davis insisted that there was not "a cigarette paper" in difference between the public statements of himself and Chancellor Philip Hammond on issues like migration or the transition to Brexit.
The Brexit Secretary suggested that EU27 residents will still be able to take complaints about Britain's use of the European Arrest Warrant to the European Court of Justice after withdrawal.
"Our view on appropriate jurisdiction is territorial," he told the committee. "If we issue a European Arrest Warrant - if we have some analogue after 2019, as I think we will have, or 2021 if that's when the transition runs out, if we have some analogue after the conclusion of our negotiations and departure - then you would expect within the European Union that to be subject to appeal all the way up through the national courts and then to the ECJ.
"If a Polish police force submits a request for anyone in Britain, that will go up to the British Supreme Court.
"We have similar arrangements with the US with extradition arrangements."
The same procedures would apply if the UK requested data on a resident of the EU, he said.
British courts would be able to take the ECJ's rulings into account when reaching their decisions, but would not be bound by them, he said.
"I would expect British courts to look at European case law, but not be bound by it," he said. "That is the point. It's not being bound by another court."