Her plea came as MPs prepare to vote on the motion in the House of Commons.
The move is expected to receive the two-thirds majority it requires for May to overturn the UK's Fixed Term Parliaments Act, which would have seen an election being held only in 2020.
"I trust the British public. I am asking them to put their trust in me and if they do that, if they give me a mandate for these negotiations for the plan for Brexit that the Government has, the plan for a stronger Britain beyond Brexit that we have, then I think that will strengthen our hand," 61-year-old May said.
The Prime Minister had stunned the UK when she called for a snap poll in an announcement yesterday.
May has framed the election, in which her ruling Conservative party could win as many as 100 extra seats,as a way of securing the best possible Brexit deal for the UK.
The Scottish National Party (SNP) has signalled its MPs will abstain in the vote and Labour and the Liberal Democrats, while accusing May of political opportunism, have welcomed the prospect of an early election.
May, who had taken charge as Prime Minister just weeks after Britain's voted to leave the European Union in June 2016, had repeatedly dismissed the idea of an early election.
However, yesterday she said she had a "change of heart" in order to bring unity within the political corridors of Britain.
May has also ruled out taking part in TV debates with Corbyn and her other political opponents, saying she believed elections were all about "getting out and about and meeting voters" and, in her words, "knocking on doors".
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