LONDON — Nigel Evans, the senior Conservative member of Parliament who has been questioned by the police over accusations of rape and sexual assault involving two men, said Sunday that the allegations were “completely false.”

In a statement to reporters outside his house in the Lancashire County village of Pendleton, Mr. Evans said the complaints were four years old and were made “by two people who are well known to each other and who until yesterday I regarded as friends.”

Mr. Evans, 55, was interrogated by the Lancashire police for most of the day on Saturday and was released with an order to return for further questioning next month. He has not been charged. The police also searched his car and house.