May has confirmed five of her most senior ministers will remain in their pre-election roles, but has yet to announce whether there will be any changes to other jobs within her top team of ministers, known as the cabinet.
But Mr Corbyn was not impressed with this arrangement and thought it lacked credibility.
"The mandate she's got is: lost Conservative seats, lost votes, lost support and lost confidence", he said.
'I can still be prime minister.
Joint chiefs of staff Nick Timothy and Fiona Hill formed part of May's small inner circle and were blamed by many Conservatives for the party's lackluster campaign and unpopular election platform, which alienated older voters with its plan to make them pay more for long-term care.
MARTIN: But she is talking to a party out in Northern Ireland called the Democratic Unionists in an effort to form a coalition that would allow her to govern.
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But despite agreeing to talk with the Tories, the DUP stopped short of agreeing to enter a formal coalition - meaning the pact is far from "strong and stable". It does not care about domestic United Kingdom politics, save to the extent that it would prefer a strong and stable government that will not be overruled by its parliament, or overly influenced by other stakeholders who do not like the compromises that are required to be made. "Chaos seems to be complete now", added Sophia in 't Veld, a Dutch MEP who is involved in the negotiations for the European Parliament. Some parliamentarians in both the Conservative and Labour parties want to remain in the EU.
The result, as the general election showed, is a muddle. European Union officials have warned talks shouldn't be delayed and have expressed their fear that with the government weakened by the election result the talks could become even more complicated.
Any such arrangement would be fraught with political risk for May, fuelling uncertainty among businesses over what the final terms of Britain's departure from the European Union would look like, and how it will affect future trade with the bloc.
The two men in charge of Britain's economy deliver their annual Mansion House speech on Thursday when they are likely to try to calm businesses and investors anxious by May's precarious grip on power and the uncertain outlook for the United Kingdom economy which has lost a lot of its momentum of 2016. "She should consider her position".
May continued to organize her government on Saturday. However, this time it was different: When May put forward her track record as home secretary, it backfired again.
Questions were then raised about whether she was a weak leader. The result ended his career and shocked Europe.
Her party's losses mean there is no longer a parliamentary majority behind such a hard Brexit and Conservatives on Friday suggested that she may have to soften her approach, perhaps by seeking to keep Britain inside the single market and the customs union.