The EU Parliament's chief Brexit negotiator has told Sky News that Britain cannot "abuse" the security of citizens to get a favourable exit deal.
Guy Verhofstadt said Theresa May's Article 50 letter was "very constructive generally" but that the security "threat" was unacceptable.
He said: "A big mistake that we could make from both sides is to start with launching threats to each other.
"I find the letter of Mrs May very constructive, generally, but there is also one threat in it, in saying 'look, we want also to co-operate with you on security issues in our common fight against terrorism but you have to give us a good deal on trade and economy'.
"It doesn't work like that - you cannot use, or abuse, I should say, the security of citizens to have then a good deal on something else."
Earlier, Brexit Secretary David Davis told Sky News Mrs May was not using security as "a bargaining chip".
He said: "What she said was that if we don't have a deal, it's not good for either side."
Mr Davis said that as one of the longest-serving home secretaries in modern history, Mrs May took the issue very, very seriously.
He said: "We are going to have, going through this process, lots of times where we say 'this is a good outcome, this is a bad outcome'."
Mr Verhofstadt, a former Belgian Prime Minister and now a key player in the upcoming negotiations, said that the UK was being "very naive" to think that an exit and trade deal can be conducted in the timetable available.
He said: "You need to do the withdrawal agreement and you have to have an agreement on what I should call the 'general terms' of your future relationship.
"Not on the detail, not on the content - that is impossible in 14-15 months to do so. We need the whole transition period of two, three, four years to fill in the content of this new association agreement for the future."
He echoed the words of German Chancellor Angela Merkel who said on Wednesday that the divorce process must be concluded before any trade deals can be negotiated.
Mr Verhofstadt said the EU was not in the mood to "punish or take revenge" on Britain - but he warned the 27 remaining nations could not allow the UK to be better off outside the bloc.
He said: "We are tough on one issue as the European Parliament, which is that we can never accept that you have a status outside the European Union more favourable than membership inside the European Union. So on that we will be unflexible."
The former Belgian PM refused to be drawn on a number for the UK's "exit bill" - with the EU rumoured to be expecting around £50bn.
He said: "What you need to do is make an agreement with each other on a number of key principles - 'sound accounting principles' - and when you have an agreement on that, then you apply them and you have a figure at the end. That's the way to go forward."
He said MEPs wanted to move quickly to protect the rights of citizens across the EU - including finding a way to allow UK citizens to keep EU membership rights.
"We need to examine what we can do for these UK citizens who want keep a link with EU citizenship. It is the citizens who are the victims of this whole political battle and we have to stop this," he said.
"We have to find a new relationship we think an association agreement is the best way to go forward."
The European Parliament, which has the power of veto on the divorce agreement, will vote next week in Strasbourg on its negotiating red lines.