May had promised to take Britain completely out of the bloc's common trading area and slash the number of people coming from the EU.
According to the statement issued on Thursday, the European Union and the United Kingdom are set to begin negotiations on Article 50, which was triggered on March 29 and sets out the procedure for withdrawing from the 27-member bloc, reports Efe news.
"We believe that the withdrawal process can not be concluded without the future relationship also being taken into account", the spokesman said.
"Our view is that a withdrawal agreement and terms of the future relationship must be agreed alongside each other", the department said in a statement Friday.
And to take into account our positions (as fast as) possible so we can start these negotiations, because that's the will of the Europeans... the representatives of the European Union, to start (as fast) as possible these negotiations.
Meanwhile, there is open debate about how Britain should approach talks with the European Union, despite a year having passed since voters chose to pull the United Kingdom out of its most important export market.
"My preoccupation is that time is passing, it is passing quicker than anyone believes because the subjects we have to deal with are extraordinarily complex", he said, according to the Financial Times.
As you know... from the side of the European Parliament, we have always welcomed a very close relationship in the future with the United Kingdom.
The first big question asks whether the government led by Prime Minister Theresa May will leave the single market or will it adopt a softer approach.
The Government has legal right and imperative to get on with these negotiations.
Since May's Conservative Party failed to win a majority in last week's general election, there has been a lot of debate over the impact on the Brexit discussions and whether the British government will be more open to compromising on some issues, like trade.
Former Tory prime minister and staunch Europhile, John Major, joined a growing list of critics of the Prime Minister's "hard" Brexit strategy by suggesting the electorate rejected that approach last Friday.
"Combined with the fact Article 50 was triggered on an arbitrary date, starting the clock on Brexit without a proper plan, it is clear that bold measures are needed to ensure we negotiate the best possible Brexit deal".
"It is clear that the Government can no longer seek to silence opposition or sideline Parliament", said Sir Keir.