Talks between UK Prime Minister Theresa May's government and the opposition Labour Party are slated to resume on Tuesday as MPs return to Westminster following the Easter break.
Cabinet ministers will meet senior opposition figures in an attempt to solve the impasse by finding a deal that could win the support of MPs, reports the BBC.
But some MPs from the ruling Conservative Party are upset that the talks with Labour are even taking place.
Leading backbencher Nigel Evans called on May to step down as Prime Minister "as soon as possible".
"The only way we're going to break this impasse properly is if we have fresh leadership of the Conservative Party," he told the BBC.
"If there was an announcement today by the Prime Minister then of course we could start the process straight away."
May is due to chair a cabinet meeting on Tuesday morning, and her de facto deputy, David Lidington, will attend the talks with Labour later.
The UK has been given an extension to the Brexit process until October 31 which means that the country is likely to hold European Parliament elections on May 23.
The Change UK will launch its European election campaign in Bristol on Tuesday, while Nigel Farage's Brexit Party will unveil its candidates in London.
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