Fylde MP Mark Menzies has pledged to carry on in his role, following allegations published in a Sunday newspaper.
Mr Menzies resigned as Parliamentary Private Secretary to International Development Minister Alan Duncan after claims reportedly made by a Brazilian male escort to a tabloid title last week.
In a statement, Conservative MP Mr Menzies pledged to continue his constituency work.
He said: “I have been going through an extremely difficult period in my private life recently, but the comments of support I have received from friends, colleagues and constituents since the weekend have been deeply moving.
“People may never know how much their words of support and friendship, including from many I have never met, have meant to me and I thank them from the bottom of my heart.”