Donald Tusk says an orderly exit is in "everyone's interest"
European Council president Donald Tusk has ruled out free EU trade access for the UK without also allowing freedom of movement.
European Union leaders are gathering in Brussels again to continue their first post-Brexit meeting.
But the British Prime Minister David Cameron is not attending the talks.
The European Council's president Donald Tusk says Britain cannot pick and choose which parts of the EU it wants to keep.
His remarks were echoed by Enda Kenny, who said the best case would be if the UK gets access to the single market - but it would have to accept freedom of movement.
The Taoiseach also suggested that other European member states are aware of Ireland's concerns about any potential loss of trade between Ireland and the UK.
All member states vowed to remain cordial and friendly with the UK, but German Chancellor Angela Merkel said that their efforts would be concentrated on protecting the future of the EU and the euro.
Earlier yesterday, Mr Cameron said he hoped Britain can continue to cooperate with Europe in areas of trade and security.
Speaking after the first day of the summit - which was attended by Mr Cameron - EU Council President Donald Tusk said the process of an orderly exit is in "everyone's interest."
While Mr Cameron said: "Britain will be leaving the European Union, but we will not be turning our backs on Europe."
The European Union has been told to "wake up and smell the coffee" after the British vote.
The call was made by the President of Lithuania Dalia Grybauskaite as she arrived for a European Council summit in Brussels.
She told reporters: "Of course this morning we all need to wake up and smell the coffee, and the coffee will be discussions on our future."
EU leaders are meeting informally to discuss the implications of the UK referendum after David Cameron outlined the UK's position on Tuesday.
The European Commission president Jean-Claude Juncker has urged the UK to begin the leave process as soon as possible.
But Mr Cameron has said it will be up to his successor to decide when to trigger Article 50 of the Lisbon Treaty.
Scotland's First Minister Nicola Sturgeon flew to Brussels to explore ways of keeping her country in the union.
She has already met European Parliament president Martin Schulz and is scheduled to have talks with Mr Juncker later.
She said it was "a pleasure" to meet Mr Schulz and a "good opportunity for me to set out Scotland's position and Scotland's desire to remain within the European Union."
Ms Sturgeon's visit comes after MSPs gave her a "mandate" to hold discussions with EU institutions, as well as the UK government and other devolved nations.
She has said that "everything must be on the table to protect Scotland's place in Europe" after the UK voted to leave the EU, although a majority of Scots voted to stay.