The chief Brexit representative for the European Parliament has said that the basic principle driving Britain and the EU's new relationship should be to put "citizens first".
European negotiator Guy Verhofstad told a news conference the parliament was "completely against citizens becoming bargaining chips in negotiations."
"When we talk about citizens, it's citizens in Britain and citizens in the European Union," he said. "It's an absolute priority that the rights of these citizens is settled."
We want the EU-27 to examine hot to mitigate the negative effects for those British people who are losing their European citizenship.
Verhofstad said that the EU and Britain should agree on a general framework of a new relationship withing two years. Britain can change its mind on leaving the EU - if all other EU states agreed to its return, he added.
President of the European Parliament Antonio Tajani has said that a "no deal" Brexit scenario would be a "catastrophe for all - but especially the United Kingdom."
"The UK would be faced with tariffs, uncertainty for the car industry and financial services, increased food prices, high traffic disruptions, long lines of lorries in Dover to name just a few," he told a news conference.
The veteran Italian politician said the UK will have to fully respect its treaty obligations until the last day of membership, including its financial commitments.
"The UK will not be asked to pay for anything they had not previously agreed to," he added.
Tajani described Wednesday as a "bad day" after Britain informed the European Council of its intention to leave the European Union.
The key European Union Brexit negotiator with the UK has said his team is "ready".
Michel Barnier also tweeted a photograph of his team who he said would "work for the 27 European Union members" during Brexit negotiations.
ITV News' Security Editor Rohit Kachroo said the letter from Theresa May triggering Brexit negotiations suggests the UK will focus on security as a negotiating tactic.
"Alongside economy, frequent mentions of security and terror in PM's article 50 letter," he said. "Clearly, UK will use its security clout as leverage."
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The 27 other members of the European Union have vowed to "act as one and preserve its interests" in Brexit talks with the UK.
A statement issued by the European Council said the talks would start by focusing on arrangements for an "orderly withdrawal" from the bloc.
The council, pledged to approach the talks constructively and hoped the UK would be a "close partner" after Brexit.
"We regret that the United Kingdom will leave the European Union, but we are ready for the process that we now will have to follow.
"Our first priority will be to minimise the uncertainty caused by the decision of the United Kingdom for our citizens, businesses and member states."
European Council President Donald Tusk has received the letter from Theresa May triggering Article 50.
At a press conference in Brussels he said "there is no reason to pretend that this is a happy day, either in Brussels or London".
He added: "After all, most Europeans including almost half the British voters wish that we would stay together not drift apart."
Mr Tusk went on to say "as for me I will not pretend I am happy today".
"There is nothing to win in this process and I am talking about both sides. In essence, this is about damage control," said Mr Tusk.
The European Council President said the EU has been strengthened by the UK leaving as "we are more determined, more united than before".
He added a final message to Britain: "We already miss you, thank you and goodbye".
Jeremy Corbyn has said Labour will ensure the Government is held to account at every stage of the Brexit.
He told the Commons Theresa May is "threatening to take this country in is both reckless and damaging".
He added he would not give the prime minister a "free hand" to use Brexit to attack rights and cut services.
The contents of the letter to the European Union signaling Britain's intent to leave the EU have been revealed.Read the full story ›
A German government spokesperson has said that Britain will remain "an important partner in NATO and as a European partner" after Brexit.
As the Prime Minister triggers Article 50 taking Britain out of the EU Germany added that both the UK and the EU have an interest in "keeping good relations".
The Germany Foreign Ministry spokesperson however criticised the two-year timetable as "damn narrow".
Issues that need clarification include the right of EU citizens in Britain, said the spokesperson adding that "uncertainties are bad for Britain and the EU".
"We are watching carefully constitutional developments in Britain, including possible Scottish Independence Referendum", they added.