He said the pressure had been affecting his family and his health and insisted the decision was his own, made after consultation with his family and constituency officers.
In the statement Mr Morley said: "The last two weeks have been traumatic for me and I have to think of my family and my health, both of which have suffered.
"Nor do I want in any way to undermine the strong position the Labour Party has in this constituency in what will be a crucial election."
Mr Morley added that he had made a "genuine mistake" and insisted that he believed he would be cleared of any wrong-doing.
After Mr Morley was asked why he did not step down immediately, he repeated his actions had been without malice and that there was still work to be done for his constituents.
He said: "I have never tried to duck responsibility for my mistake and have repaid the amount in full.
"I understand people's anger over the whole issue of MPs' expenses.
"For those who condemn me I would simply ask to be allowed the opportunity to present my case."
Following Mr Morley's statement, the constituency chairman Mick Grant said: "Elliot has been a long-standing and committed MP for Scunthorpe.
"He has always had our full support and will be a hard act to follow."
Mr Morley, a former agriculture minister, has already been suspended from the Parliamentary Labour Party and referred to the party's disciplinary panel.
Prime Minister Gordon Brown has described the allegations against him as "serious".
The Telegraph also alleged Mr Morley rented out a London flat designated as his main residence to another Labour MP, Ian Cawsey, a close friend and former special adviser.
Mr Morley said he used the money from his Labour colleague to reduce his claim to the taxpayer.
Since the Daily Telegraph began its reports on MPs' expenses - based on leaked receipts - 13 MPs, including Speaker Michael Martin, have announced their intention to stand down.
In an interview with the Daily Telegraph, Tory leader David Cameron said any MP who had committed a crime with their expenses claims should "face the full force of the law".
He added Scotland Yard, which is considering whether to launch criminal inquiries into potentially fraudulent claims, should examine them "without fear of favour".
Meanwhile, a Populas poll in Saturday's Times newspaper, has suggested Labour is at its lowest ever national rating following the expenses expose.
Labour trailed in third place after the UK Independence Party with just 16% of respondents prepared to vote for them in next weekend's European elections.
BBC political editor Nick Robinson said: "If that [projection] was to be repeated in next Sunday's results, it would have serious consequences for Gordon Brown and raise serious questions over how and whether he can help his party recover."
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