Theresa May's ministers have tried to play down a row with key players in Brussels over an apparent threat to pull security co-operation unless the European Union agrees a trade deal.

Brexit Secretary David Davis insisted that his counterparts on the continent had praised the "positive" letter the Prime Minister sent to invoke Article 50, and it was simply stating that a replacement for current crime and security measures would need to be negotiated.

Critics accused the Prime Minister of trying to make a trade-off between security and commerce by mentioning the crime-fighting measures alongside a trade deal in her letter.

But Mr Davis said: "I spent all of yesterday afternoon on the telephone talking to my opposite numbers in the Parliament, in the commission, around all the member states.

"Virtually all of them said spontaneously, it's a very positive letter, the tone was good, and so on."

He told ITV's Good Morning Britain: "One part of the deal is the justice and home affairs strand, we currently have arrangements for exchanging information, for arrest warrants, for Europol and all those things.

"We will need to replace that with something else because that will go when we leave the European Union."

Mr Davis said it was a "negotiation" and "the other side might want to change things too".

The reference to security caused concern in Brussels.

Asked if he thought Mrs May was engaged in "blackmail", the European Parliament's co-ordinator for Brexit Guy Verhofstadt said: "I try to be a gentleman, so towards a lady I don't even use or think about the word 'blackmail'."

But Mr Davis played down the issue, saying: "Guy Verhofstadt called it blackmail, let's not say everybody did."

Work and Pensions Secretary Damian Green said the row was a "misunderstanding".

The two issues had been mentioned side by side because they were "all bound up in our membership of the European Union", he said.

"It's not a threat, I think that's the misunderstanding," he told BBC Two's Newsnight. "It's absolutely not a threat."

The next stage of the Brexit process will see plans set out to repatriate more than 40 years of powers back to Westminster, with the publication of the details of the Great Repeal Bill.

The white paper - Legislating for the United Kingdom's withdrawal from the European Union - will set out how the Government will deal with EU laws that cannot be easily converted.

Secondary legislation, known as statutory instruments, will be used to make technical changes, with up to 1,000 pieces expected, nearly as many as MPs and peers usually deal with in an entire parliament.

Mr Davis said the reference to weakened security co-operation was "not a threat" to the 27 other EU members.

"This is a statement of the fact that this would be harmful for both of us, if we don't get a deal.

"It's an argument for having a deal, and that's what we are after," he told BBC Radio 4's Today.

"We are after a fully-comprehensive deal that covers trade, that covers security, covers all the aspects of our existing relationship and tries to preserve as much of it - the benefits for everybody - as we can."

He acknowledged there was a dispute over the way the negotiations with Brussels would proceed.

The Article 50 process states that the negotiations must "take into account" the future relationship along with the withdrawal arrangements, he said.

"The commission has taken a different stance and said 'we want to deal with the departure first and the ongoing relationship second'. There is an area of argument over this, an area of discussion over this, which is fine."

France's ambassador to the UK Sylvie Bermann said there could be no "trade-off" over security and a free-trade agreement (FTA).

She told Today: "We are all facing the same security challenges and we all need security. So it can't be a trade-off between an FTA, an economic agreement, and security."

Mr Verhofstadt told Good Morning Britain: "What I think is not possible is to say to the European Union 'well look we will only co-operate on security if you give us a good trade deal or a good economic package', that is not done.

"The security of the citizens is so important, the fight against terrorism is so crucial, that you cannot negotiate with something else.

"What we propose is to make an association agreement between the UK and the EU with two consistent pillars, one on security, the fight against terrorism, external and internal; and at the other hand a good trade deal, a fair trade deal, where it is clear naturally, that outside the European Union, you can never have a status that is so favourable than a member state of the European Union."

Asked about his promise that the UK's trade deal would provide the "exact same benefits" as membership of the single market, the Brexit Secretary said: "I make no apology for being ambitious about what we are trying to do."

He added: "I want the best possible benefits from the European Union, I also want the best possible benefits in terms of world trade - the real prize to be had in this, the ability to do deals with the fastest-growing, the biggest markets in the world."

But he acknowledged that "achieving it, of course, is a matter of negotiation, and negotiations are uncertain".