The UK Cabinet still supports talks with the Labour Party as a way to find a Brexit solution, according to the spokesman.
The statement comes after Theresa May stated on 1 May that she had not been planning to change her strategy on Brexit despite her Conservative Party's losses in the recent local elections, stressing that withdrawing from the European Union with the deal they had negotiated was the "best possible outcome".
Theresa May's Brexit deal with Brussels has already been rejected three times by parliament, yet the PM hopes to negotiate a way forward with Labour to break the deadlock.
In April, EU leaders decided to provide the United Kingdom with a flexible Brexit extension until 31 October, which means that London will be able to withdraw from the bloc before the set deadline if the withdrawal agreement is ratified by the UK Parliament. It was also agreed that the United Kingdom will have to hold European Parliament elections in May, if it is still a member of the bloc, or leave the union on 1 June.