Labour leader Jeremy Corbyn has called on May to resign, but May made no direct comment on her immediate future as either Prime Minister or Conservative leader.
Her voice cracking with emotion after she was returned as MP for Maidenhead, May said: "The country needs a period of stability", adding: "It will be incumbent on [The Conservatives] to ensure that we have that period of stability and that is what we will do."
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She said that, while votes are still being counted, she remained confident that her party would secure the most seats and the most votes.
Officials at home secretary Amber Rudd's seat of Hastings and Rye are currently engaging in a recount.