Mark Menzies, 42, quit as a parliamentary private secretary to International Development Minister Alan Duncan after a newspaper published the allegations.
The Fylde MP made no further comment at his home in St Annes, Lancashire, hours after he announced he had quit.
Mr Menzies, originally from Irvine, North Ayrshire, said: "I have decided to resign as a PPS after a series of allegations were made against me in a Sunday newspaper. A number of these allegations are not true and I look forward to setting the record straight in due course."
The former chair of Fylde Conservatives, Councillor Brenda Ackers, said: "He's obviously very shocked and needs time to consider his answer to these allegations.
"He has the total support of myself and two other members of the management team, they both support Mark also.
"The wider membership has not been spoken to, I think probably a lot of them don't know anything yet."
Defence Secretary Philip Hammond said: "It's always very sad when people are involved in personal issues that impact on their careers, but that's a matter for the person concerned."
Tory MP David Ruffley told reporters: "Government rocked? I don't think so."
Mr Menzies was elected in 2010 and was swiftly promoted to be a ministerial aide, serving former energy minister Charles Hendry and former housing minister Mark Prisk before his role with Mr Duncan.
A Glasgow University graduate, he was raised by his mother after his father died a month before he was born. He previously worked for Marks & Spencer as a graduate trainee.