The Commons standards watchdog has been asked to examine claims that three former News International executives lied to MPs examining the phone-hacking scandal.
Ex-News of the World editor Colin Myler, the paper's former legal manager Tom Crone and one-time News International executive chairman Les Hinton were accused of misleading the Culture, Media and Sport Select Committee during its investigation of the events.
The men have denied the allegations but the committee's chairman John Whittingdale said they were "very serious matters" which should be investigated by the Standards and Privileges Committee of MPs.
The Commons agreed without a vote to refer the phone-hacking report's conclusions to the Standards and Privileges Committee, which has the power to recommend sanctions against the trio and News International.
Although there is the possibility of the three men being summoned to the Commons for a public dressing-down, Labour MP Chris Bryant said the Standards and Privileges Committee should also consider fines or imprisonment as possible penalties.
Mr Whittingdale said the committee agreed unanimously that the three misled MPs - and revealed "alarm bells began ringing" when it was claimed the hacking scandal was limited to one journalist - News of the World royal editor Clive Goodman, who was jailed in 2007 for conspiring to listen to voicemails.
He said documents handed to his committee showed the so-called "rogue reporter defence" was false.
Mr Whittingdale said: "The evidence we obtained made it very clear that the individual who had given evidence to us in our previous inquiry - where they had once again attempted to assure us that there was no real suggestion or evidence obtained that anybody else at the News of the World was involved in phone hacking other than Clive Goodman - was not true.
"They certainly did have documents which indicated very clearly that that was not the case.
"It was for that reason that the committee concluded that we have been misled by the three individuals."
He said it would be for the Standards and Privileges Committee to decide what punishment the trio should face, but called for the misleading of a parliamentary committee to "bear profound consequences".
He added: "I'm not entirely sure what the consequences are, but there is no question that these are very serious matters."
Labour deputy chairman Tom Watson, who sits on the committee and fought to expose the phone hacking scandal, said MPs could censure other witnesses once criminal proceedings end.
Mr Watson said: "We are united in making sure the three people named receive some sort of parliamentary justice.
"The last thing we want to do is interfere with the process of criminal justice that is taking place."
Commons Leader Sir George Young backed the motion and said select committees only worked if witnesses told the truth.
But he said the Standards and Privileges Committee should deal with any punishment "having regard to the House's 1978 resolution to use its penal jurisdiction in respect of non-Members as sparingly as possible and only when the House is satisfied that it is essential to act in order to provide reasonable protection from improper obstruction causing or likely to cause substantial interference with its functions".
The Government last month launched a consultation in an attempt to clarify what sanctions were open to Parliament.
It noted that the Commons' power to issue fines was last used in 1666 and may have lapsed and that no non-MP had been punished by the House since a 1978 agreement to use penal powers sparingly.
The last member of the public to be summoned to the bar of the House of Commons was Sunday Express editor John Junor who appeared before MPs in January 1957.
The newspaper had published a piece criticising petrol allowances given to political parties in constituencies.
He was rebuked by MPs for failing to "establish the truth of the article" and not being willing to "admit its obvious implications". He apologised and no further action was taken.
The last fine imposed on an offender by the House was on February 6, 1666 when Thomas White was ordered to pay £1,000 for causing an MP to be arrested and prevented from attending Parliament.
The last imprisonment by the Commons of a non-member was of Charles Grissell in 1880 for a breach of privilege in connection with the committee on the Tower High Level Bridge (Metropolis) Bill.
Mr Bryant said he believed the case would prove to be "one of the most flagrant examples of a contempt of Parliament in Parliament's history".
"It is not just that it was one person at one time, it was not just that it was one organisation for a brief period of time, it's that a whole series of people systematically, repeatedly lied so as to protect themselves, to protect their commercial interests and to try and make sure they didn't end up going to prison - that they did fully knowing that they were telling lies to parliament.
"That, I believe, is a fundamental contempt."
He added: "I believe that this House and the committee itself should consider in turn, firstly whether or not the three individuals mentioned, and corporately News International should be summoned to this House. I believe that it must still be an important power for this House.
"Secondly, they should consider whether individuals should be fined, not least because there have been considerable expenses incurred by Parliament and the prosecuting authorities by the process of lying to Parliament, and thirdly, it has to be right whether or not to imprison.
"If this had happened in the Scottish Parliament it would have gone on to imprisonment, if it had been a contempt of court it would have led to imprisonment, if it had been perjury of a court, it would have led to imprisonment."
Liberal Democrat MP John Hemming said: "We are elected here to represent our constituents. The privileges of Parliament are their privileges.
"If we don't act when people lie to Parliament, we are failing our constituents."