Deputy Speaker Nigel Evans has been released on bail after being arrested on suspicion of the rape and sexual assault of two men.
The Conservative MP, a prominent gay rights campaigner, is expected to respond to the allegations later, in person, in a statement.
Earlier, the 55-year-old posted a message on his Facebook page thanking members of the public for their support.
He wrote: "thanks for the amazing overwhelming support at this difficult time...."
Mr Evans was arrested on Saturday morning at his constituency home in the village of Pendleton, near Clitheroe, in Lancashire.
The politician was questioned by police over an allegation of raping one man and sexually assaulting another between July 2009 and March 2013.
After several hours in custody in Preston, Mr Evans was released on bail at 10.30pm and asked to return to the police station on June 19.
Prime Minister David Cameron and Speaker John Bercow were informed of the arrest of the popular MP.
Sky News Crime Correspondent Martin Brunt said: "The allegations are one of rape against one man and sexual assault against another man. Both of those men are now in their early 20s."
He said: "The offences are said to have been committed at his home in the village of Pendleton near Clitheroe which is in his constituency of Ribble Valley."
Mr Evans, who comes from Swansea and whose parents ran a newsagents, has been MP for Ribble Valley since 1992.
Politicians and constituents said they were "shocked" by the allegations.
Michael Ranson, the chairman of the Ribble Valley Conservative Association, told Sky News: "He is a very popular MP and a very good constituency MP.
"He's given assistance to a lot of his constituents over many years. Everybody's completely shell-shocked."
Brian Binley, Tory MP for Northampton South and a friend of Mr Evans, said: "I was just deeply disturbed and shocked.
"I've known him ever since I've been in Parliament and I came in in 2005. I consider him to be a very good friend.
"I know him to be caring, compassionate and in no way would he inflict himself violently on any other person."
Mr Evans has held a number of front bench posts for the Conservative Party and was a Parliamentary Private Secretary in John Major's government and his spokesman for Welsh Affairs.
In 2010 he became one of three deputy speakers, earning £102,000-a-year, including his MP's salary.
In December 2010 he came out as gay in an interview with the Mail On Sunday newspaper in which he said that he was "tired of living a lie".
Mr Evans, who was vice chairman of the Conservative Party from 1999 to 2001, said he had been threatened with exposure by political opponents.
Sky News Chief Political Correspondent Jon Craig said: "Since then he has become quite a prominent gay rights campaigner.
"He had held, for example, at least one function in the Speaker's apartments on gay rights.
"John Bercow let him use the Speaker's apartment for a function and he has been prominent in that campaign.
"He is a very sociable MP. He is very well known."
A villager who lives opposite the MP and who did not want to give her name said: "I am shocked. I like him. He is a good MP and he has done a lot for the Ribble Valley.
"Obviously he is well known in the village and goes to the local pub a lot."
Another Pendleton resident, who also did not want to give his name, said: "It's unbelievable, I know him very well. He is an excellent person and I would stand by him 100%."
A Lancashire Police statement confirmed that a 55-year-old man from Pendleton had been been arrested on suspicion of rape and sexual assault and that he was being interviewed by officers.
The statement said: "We take all allegations of a sexual nature extremely seriously and understand how difficult it can be for victims to have the confidence to come forward.
"As a constabulary, we are committed to investigating sexual offences sensitively but robustly recognising the impact that these types of crimes have on victims.
"We would encourage anyone who has experienced sexual abuse, or who has information about it, to have the confidence to report it to us knowing that we will take it seriously, deal with it sensitively and investigate it thoroughly."