Keith Vaz, Commons Home Affairs Select Committee chairman, said it was acting after John Yates, one of Britain's top police officers, raised questions over the law as he gave evidence to the committee this morning.
The inquiry will focus on the police response, the ease of prosecuting such offences, and the treatment of victims after it emerged the New York Times refused to co-operate with British police looking into allegations of phone-hacking made by the newspaper last week.
Mr Vaz said: "The evidence of Assistant Commissioner John Yates today raised a number questions of importance about the law on phone-hacking, the way the police deal with such breaches of the law and the manner in which victims are informed of those breaches.
"I hope that this inquiry will clarify all these important areas."
The committee's inquiry will be the second time MPs have investigated the issues surrounding the 2007 convictions of News of the World reporter Clive Goodman and private investigator Glenn Mulcaire for illegally intercepting the voicemail messages of Princes William and Harry.
The Department for Culture, Media and Sport select committee previously described the "collective amnesia" of News of the World journalists when asked about their recollections of the time.
The Home Affairs select committee will focus on the "definition of the offences relating to unauthorised tapping or hacking in the Regulation of Investigatory Powers Act, and the ease of prosecuting such offences".
It will also consider "the police response to such offences, especially the treatment of those whose communications have been intercepted" and "what the police are doing to control such offences".
Earlier today, Mr Yates said the Met would press ahead with questioning former reporter Sean Hoare and consulting with prosecutors over whether to reopen its investigation into the News of the World.
In interviews with the New York Times (NYT) and the BBC, Mr Hoare claimed that eavesdropping on voicemail messages was widespread at the News of the World and known to the then editor Andy Coulson - now Prime Minister David Cameron's director of communications.
His claims are denied by both the News International-owned newspaper and Mr Coulson himself, who has offered to speak to police.
Mr Yates told MPs he expected to see Mr Coulson "at some stage", but would not decide whether to take up his offer until after Mr Hoare has been interviewed.
Officers wrote today to the NYT asking the US paper to reconsider its decision not to hand over information, citing "journalistic privilege", but Mr Yates said he was "not hopeful". It was an article in the New York paper which revived the phone-hacking issue last week.
Mr Yates came under fierce questioning from MPs on the select committee over the police's decision not to contact some 91 people - believed to include politicians and celebrities - whose voicemail Pins were discovered during the investigations into Goodman and Mulcaire.
He said police or mobile phone service providers had contacted around 10 to 12 people in cases where they thought there was "the minutest possibility" that an attempt had been made to hack into their messages.
The assistant commissioner promised to speak to Labour MP Chris Bryant, who complained in the Commons chamber yesterday that he had been told he was on Mulcaire's list, but police had done "absolutely nothing" about it.
Mr Yates defended the initial police inquiry, telling MPs: "You may not believe it but I still think the investigation was a success, and if HMI (the Inspector of Constabulary) wants to come and have a look at it, I wouldn't have a problem at all."
The jailing of Goodman and Mulcaire had sent out a "very significant deterrent message" and the case clarified the law relating to interception of communications, he said.
Mr Yates acknowledged that there had been cases of police officers taking payments from newspapers for information, but said he regarded it as "reprehensible" and insisted it was not widespread.
Mr Yates repeated his assurance that former deputy prime minister Lord Prescott's mobile phone had not been hacked into and said there was no evidence that any MP's phone had been tapped.
It was a "dangerous assumption" to believe that any particular individual named on lists seized during the police investigation was necessarily the victim of eavesdropping, he warned MPs.
Phone-hacking was very narrowly defined in legislation and was "very, very difficult to prove", he said.
Leading counsel had advised police that obtaining a Pin without the owner's permission was not in itself a crime, said Mr Yates.
But committee chairman Keith Vaz told him that this would be a breach of the Data Protection Act.
He urged him to contact all those whose details were found on Mulcaire's lists: "They are the victims of crime in the same way as if someone's bank account has been hacked into. You would write to those people and inform them."
Mr Vaz added: "I think it is the feeling of this committee that there are some questions which remain to be answered."
Mr Yates stressed that it had not yet been decided whether to mount a fresh investigation in the light of Mr Hoare's allegations, which he said "came out of left field", as he had already left the paper before the Goodman case.
Acting Labour leader Harriet Harman has written to Met Police Commissioner Sir Paul Stephenson asking him to alert any of the party's MPs "if their name, phone number or pin number appears in the list of phones uncovered in your investigation into phone tapping by the News of the World".
Labour former minister Tom Watson, who yesterday warned Home Secretary Theresa May that British democracy risked becoming a "laughing stock" unless allegations of phone-hacking were fully investigated, called on Mr Yates to look further than just Mr Hoare's claims.
"John Yates has said that he'll investigate the new allegations made by Sean Hoare but has steadfastly refused to investigate his strongest lead - the existence of an illegally hacked phone message provided by Glenn Mulcaire and transcribed by News of the World reporter Ross Hall," he said.
"If anything in this case is a smoking gun - establishing that Clive Goodman was not just a rogue reporter - it is this.
"The Met police continues its disdainful disinclination to actually investigate this case. The public and Parliament expect answers. He should interview Ross Hall."
Mr Yates had earlier indicated to the committee he felt interviewing Mr Hall would make no difference to the inquiry.
Former News of the World reporter Sharon Marshall, who told the New York Times that hacking was "an industry-wide thing", today said it was "entirely possible" that Mr Coulson was not aware the practice was being used by his own newspaper.
In a statement, the News of the World accused the New York Times of being motivated by commercial rivalry.
It said: "The News of the World repeatedly asked the New York Times to provide evidence to support their allegations and they were unable to do so.
"Indeed, the story they published contained no new credible evidence and relied heavily on anonymous sources, contrary to the paper's own editorial guidelines.
"In so doing, they have undermined their own reputation and confirmed our suspicion their story was motivated by commercial rivalry.
"We reject absolutely any suggestion there was a widespread culture of wrongdoing at the News of the World."
It was reported that the last government decided against calling in HM Inspectorate of Constabulary (HMIC) to scrutinise the Met's probe because it would have "deeply resented" the interference.
According to the Guardian, a memo from Stephen Rimmer, the Home Office director general for crime and policing, warned that such a move would send a message that "we do not have full confidence" in the force.
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