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He has been suspended from the parliamentary party.
The Tiverton and Honiton MP had the Tory whip withdrawn on Friday.
Writing on his website, Mr Parish said: “Following recent allegations regarding an MP’s use of their mobile phone in Parliament, I have referred myself to the Parliamentary Commissioner for Standards in the House of Commons.
“I will be cooperating fully with any investigation, and whilst it is ongoing I will continue to perform my duties as MP for Tiverton and Honiton.
“I will not be making further comments at this stage.”
Later asked by broadcasters if he opened something in error in the Commons, he said: "I did, but let the inquiry look at that."
Mr Parish added that he will not remain in his position if he is found guilty.
He said he told his wife on Friday afternoon, adding: "Of course it's embarrassing and it's embarrassing for my wife and family, so that's my main concern at the moment."
His wife Sue Parish said "it was all very embarrassing" as she told the Times she was not aware of her husband having done similar activities before.
"No. He's quite a normal guy, really. He's a lovely person. It's just so stupid," she said.
Now the 65-year-old is waiting for the result of the investigation after a conversation with Tory Chief Whip Chris Heaton-Harris.
A spokeswoman for Tory Chief Whip Chris Heaton-Harris said: “Having spoken to the Chief Whip this afternoon, Neil Parish MP is reporting himself to the Parliamentary Commissioner for Standards.
“Mr Parish has been suspended from the Conservative whip pending the outcome of that investigation.”
The allegations surfaced during a meeting of Tory MPs on Tuesday.
Mr Parish is the chair of the Commons Environment, Food and Rural Affairs Committee.
He has represented the Tiverton and Honiton constituency in Devon since 2010.
Following his decision to refer himself to Commons authorities, officials said the independent standards commissioner Kathryn Stone would initially investigate Mr Parish.
A separate inquiry by Parliament’s Independent Complaints and Grievance Scheme (ICGS) is also under way meaning Mr Parish now faces two probes into his conduct.
An ICGS inquiry into an MP’s conduct can only be opened if the individuals directly involved make a complaint.
There was anger from some Tory MPs that Chief Whip Chris Heaton-Harris failed to remove the whip from the MP at the centre of the claims earlier this week and suggested the matter be raised with the ICGS.
A spokesman for the House of Commons said he couldn’t confirm or deny if the ICGS had now opened an inquiry.
He added: "Parliament’s Independent Complaints and Grievance Scheme (ICGS) operates on the basis of confidentiality for the benefit of all parties.
“Therefore, we cannot provide any information on complaints or investigation, including whether or not a complaint has been received or whether an investigation is ongoing."