Draft EU guidelines for Brexit rule out starting free trade talks with the UK before "sufficient progress" is made on other issues.
The paper presented by European Council President Donald Tusk will have to be approved by the 27 member states.
Other issues include the status of three million EU citizens in the UK and a million Britons in the EU.
Separately, another top EU official suggested the bloc could manage without the UK in defence and security matters.
The UK formally triggered the Brexit process on Wednesday after calling for simultaneous talks on exit terms and future trade ties.
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At a news conference, Mr Tusk said: "Starting parallel talks on all issues at the same time as suggested by some in the UK will not happen.
"Only once we have achieved sufficient progress on the withdrawal can we discuss the framework for our future relationship."
It is clear the UK will face a tough divorce, the BBC's Gavin Hewitt says, but there were some hints at flexibility from Mr Tusk.
- Read more from Gavin Hewitt
Talks would be "difficult, complex and sometimes even confrontational", Mr Tusk predicted, but the EU would not "pursue a punitive approach".
UK Prime Minister Theresa May formally triggered the Brexit process by sending the Article 50 notification letter to Mr Tusk on Wednesday.
The two are to meet in London ahead of an EU summit on Brexit, which will not include her, on 29 April.
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So what's the 'divorce' bill?
The draft says the EU's overall objective is "to preserve its interests, those of its member states, its citizens and its businesses".
Calling for a "phased approach giving priority to an orderly withdrawal", it suggests starting with discussions on the separation arrangement. They could then move on to talks about a future trade relationship between the EU and the UK.
The draft raises the issue of what the UK might have to pay to leave the EU, bills earlier estimated to be as much as €60bn (£51bn; $64bn).
In a sign of the bloc's determination to secure a "divorce bill", it says that a "single financial settlement should ensure that the Union and the United Kingdom both respect the obligations undertaken before the date of withdrawal".
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How will borders be affected?Image copyright Reuters Image caption
The guidelines call for "flexible and imaginative solutions'' on the issue of the UK's land border with the Republic of Ireland, with the aim of "avoiding a hard border".
As for Gibraltar, Spain will have a special say on the future of the disputed British territory, according to the guidelines.
"After the United Kingdom leaves the union, no agreement between the EU and the United Kingdom may apply to the territory of Gibraltar without the agreement between the Kingdom of Spain and the United Kingdom," they state.
Gibraltar's chief minister, Fabian Picardo, accused Spain of manipulating the European Council for its own political interests, saying this was "unacceptable".
Conservative MPs in the UK warned that the sovereignty of the UK overseas territory was non-negotiable.
- Gibraltar angered by Spain's EU 'veto'
What about the UK's security role?
Mrs May's letter had been interpreted by some as threatening to withdraw co-operation with the EU on security matters.
Speaking at a Nato meeting in Brussels, EU foreign policy chief Federica Mogherini said: "The UK contributes today only for 3% of our civilian capabilities in our EU operations and missions, and 5% to the military ones.
"So for sure it's a valued contribution, but for sure a contribution without which the European Union defence and security work can continue perfectly well."
This is the start of a two-year, cross-Channel political rollercoaster ride. The EU's draft guidelines for Brexit are uncompromising and firm.
They say they will update them "as necessary" during negotiations, meaning they are ready for anything, including, the text explicitly says, for talks with the UK to fail altogether.
Gone are the words of sadness and regret at Britain's departure. The message is: Roll up your sleeves, we're ready for you.
How did other British politicians react?
- Foreign Secretary Boris Johnson: "There's a lot of goodwill... to achieve what the prime minister has said she wants to achieve, which is an orderly transition."
- Liberal Democrat leader Tim Farron: "These guidelines show the strength of the EU in these negotiations and the carelessness of the UK government in isolating themselves from our European allies."
- Labour MP Owen Smith: "Two days into a two-year negotiation and the government's lofty rhetoric is colliding with hard reality. The prime minister's plan for Britain is a pipe dream."
- UKIP leader Paul Nuttall: "It is beholden on the UK government to get the best deal possible for the people of this country. To do so will require patience, flexibility, goodwill and imagination. Sadly none of these qualities are visible in the EU position paper."