discussions could not carry on due to "the increasing weakness and instability" of the government.
The two parties are now expected to discuss how to put a number of options to MPs to break the deadlock.
On Thursday the PM promised to set a timetable for leaving Downing Street following a Brexit vote next month.
Theresa May will try once again to gain the support of MPs in the week beginning 3 June, when the Commons votes for the first time on the EU Withdrawal Agreement Bill - the legislation needed to implement her deal.
BBC political editor Laura Kuenssberg said if the bill were defeated, Mrs May would be expected to announce that she was stepping down.
The UK was due to leave the EU on 29 March - but after MPs voted down the deal Mrs May had negotiated with the bloc three times, the EU gave the UK an extension until 31 October.
This prompted negotiations between the Tories and Labour to see if the parties could come to a Brexit agreement.
Labour's favoured plan includes a permanent customs union with the EU, meaning no internal tariffs (taxes) on goods sold between the UK and the rest of the bloc.
It also keeps the option of a further referendum on the table, giving the public a say on the deal agreed by Parliament.
Both scenarios have caused anger among Brexit-backing Conservatives, who claim a customs union would stop the UK to negotiating its own trade deals around the world and who believe another public vote is undemocratic.