He also described Brexit as the "position of the Tories", rather than the democratically expressed will of the British people, and said the United Kingdom should lose the Brussels budget rebate negotiated by Margaret Thatcher in 1984, and sovereignty "opt-outs" on borders and the euro.
Britain also enjoys opt-outs from elements of the European Union, including from ever joining the euro currency.
"We all have an interest.in keeping them as close as possible to the European Union, because Britain is an important country, vital to the EU in the security and foreign policy realm, and naturally also a part of the European market", he said.
Britain's Prime Minister Theresa May (L) and France's President Emmanuel Macron hold a joint press conference in the grounds of The Elysee Palace in Paris on June 13, 2017.
He said: "Of course the door remains open, always open until the Brexit negotiations come to an end". "The current uncertainty can not continue", he added on Twitter, urging the United Kingdom government to take the general election result "into account" and not pursue a "hard Brexit".
It had been suggested the start of negotiations could be delayed by the failure of any party to win a House of Commons majority at last week's General Election.
UK Parliament opening date set, suggesting Tory deal reached
In a statement this morning, Andrea Leadsom confirmed that the State Opening would be postponed by two days due to a delay with the making of The Queen's Speech.
European Parliament leaders laid into May and called for Britain to say when negotiations would start.
He went on to stress that once negotiations begin, moving backwards will become much more hard.
Mr Verhofstadt urged the European Union to bring forward legislative proposals for closer integration of the remaining 27 member states, to take advantage of the opportunity provided by Brexit and the election of the pro-European Mr Macron.
Mrs May said the election revealed "a unity of purpose" among British voters for the Government to get on with Brexit.
The prominent Eurosceptic said: "The reality is, where we stand follows logically from leaving".
"If we are having economic benefit that means we need to be able to control our trade policy".
Pressed on the issue of the customs union he said: "These are decisions which the Government will have to take, but I'm quite clear and I've made my position public in the past".