Talks will resume on October 7 after the EU said the UK's proposed alternative to the Irish backstop could not be the "basis" for a legally-binding treaty.
The UK has said it would work on the details before then but there was "no path" to a deal without alternative arrangements in Northern Ireland.
Prime Minister Boris Johnson has insisted the only options were a "new deal or no deal".
Earlier on Friday, he posted a message on social media saying there would be "no delay" to the UK's exit beyond the October 31 deadline.
This was despite the government stating, in papers submitted to a Scottish court, that Johnson would comply with legislation passed by Parliament, known as the Benn Act, which will require the Prime Minister to send a letter to the EU asking for a further three-month Brexit extension if a no deal was agreed by October 19 - a day after a crucial summit of European leaders.
The UK has said that its new proposals, presented on Wednesday, represent a "significant" shift and the basis for a "fair and reasonable compromise" after months of deadlock.
( With inputs from IANS )