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"At the end of this week, I am saying that there will be no sufficient progress from now until October unless miracles will happen", he said.
But British Prime Minister Theresa May insisted there had been "very good progress" on the rights of European Union expatriates, following a major Brexit speech she gave in Florence, Italy, last week.
British officials are eager for negotiations to move on to discussions about the UK's future relationship with the European Union - but speaking at the same summit, Mr Juncker said it would take a "miracle" for Brussels to agree to proceed to the next phase.
She further expressed the hope that the rights of British citizens would be ensured in other European countries, adding that she had stated earlier how Britain can ensure the rights of European Union (EU) citizens in the country.
His British counterpart David Davis agreed, saying that "it'll take weeks or possibly even months until we can say there has been sufficient progress".
Pressing her case, she met German Chancellor Angela Merkel on the sidelines of the summit and repeated her pledge for Britain to be "the strongest friend and partner to the EU" after Brexit, her spokeswoman said.
Emmanuel Macron will also attend the meeting
Trade minister Liam Fox has described EEA nationals in the UK as one of the government's "main bargaining chips" in upcoming negotiations, and May has argued that the UK would be left "high and dry" in negotiations by guaranteeing the rights of EEA nationals without receiving similar assurances for UK nationals living in the EU.
It is thought there could be an agreement with the EU which would see the United Kingdom give the go-ahead for divorce costs of £40 billion and the residency rights of Europeans in the UK. Theresa May's conference speech previous year was enough to send the pound tumbling as her words on "citizens of nowhere" hinted at a diamond hard Brexit.
In Tallinn, May sidestepped questions over whether she was confident of the October deadline.
"She chose Florence because Florentine politics in the 15th century make her feel at home, I think", he said at an event at the London School of Economics.
She said: "Our resolve to draw on the full weight of our military, intelligence, diplomatic and development resources to lead global action with our partners on the issues that affect the security and prosperity of our peoples is unchanged".
Barnier and Davis acknowledged that they had failed to bridge differences over what role the European Court of Justice should play in the future.
Speaking at the Tapa military base in Estonia this morning, the Prime Minister provided further assurances that Britain remains "unconditionally" committed to the collective defence of Europe. More than 800 British troops have been in the Estonian town of Tapa since April, alongside Estonian and French forces.