Labour leader Ed Miliband has accused David Cameron of failing "to react with the necessary speed" to the phone hacking scandal.
He urged the prime minister to "show leadership" and set up a wide-ranging, judge-led public inquiry immediately.
The government plans to announce the remit of two inquiries into the issue before Parliament's summer recess.
Meanwhile News International has announced that this Sunday's edition of the News of the World will be the last.
The company's chairman James Murdoch told staff on Thursday: "The News of the World is in the business of holding others to account. But it failed when it came to itself."
It follows reports that relatives of soldiers killed in Iraq and Afghanistan may have been the victims of hacking.
Earlier Mr Miliband said he was "absolutely horrified" by the allegations and their emergence made it even more important that an inquiry was set up quickly to investigate hacking, regulation of the press and the relationship between the police and the media.
He added: "The prime minister has a very close relationship with a number of the people involved in this...
"I think he should ignore those relationships and come out and say the right thing because that is what the country expects."
Mr Cameron has said any probe cannot actually begin until the police investigation into hacking is complete. He is due to meet Mr Miliband next Wednesday to discuss the inquiries.
Leader of the House of Commons Sir George Young said the government was planning two inquiries - one into the police handling of the original hacking investigation, and one into the actions of the media.
He said ministers would consult widely on the remit of these inquiries in the coming weeks, including with Commons privacy committee and members of other parties, and would announce their decision before the recess begins on 19 July.
Conservative London Mayor Boris Johnson is among the figures who have demanded faster action from Mr Cameron.
"I certainly think there should be a judge-led inquiry and I think it should be immediate," he told BBC Radio 4's Today programme, adding that the hacking allegations had left him with a "burning outrage".
"I think there should be no holds barred. Get the editors, get the proprietors in and let's hear exactly what has been going on."
Mr Johnson also said there should be "external validation" of the Metropolitan Police's inquiry into its own handling of the case, adding: "There has to be confidence that this is not just the police washing their dirty linen."
Labour MP Chris Bryant, who has been a vocal campaigner on hacking and secured an emergency Commons debate on the subject on Wednesday, agreed that steps could be taken now.
"I think you need a statutory inquiry to be set up now. It probably wouldn't meet in public now but it would be set up," he said.
"It would have its terms of reference [decided]. It would have the power to summon evidence before somebody starts shredding it either at News of the World of the Metropolitan Police."
Lib Dem leader Nick Clegg has also contacted all of his MPs to assure them he will be pushing for a judge to be appointed.
The Royal British Legion has severed its links with the News of the World over the latest allegations about service families.
The move follows the decision by a growing list of companies, including Ford, Boots, Asda and Lloyds, to suspend their advertising with the paper.
Asked whether the government should follow suit, Sir George Young said he would raise the matter urgently with his cabinet colleagues.
The Central Office of Information, which is in charge of government marketing, spent £53,377 in the past year on adverts in the News of the World.
Meanwhile, the government has refused to bow to pressure to suspend consideration of a bid by the News of the World's parent company to take over broadcaster BSkyB.
Asking an urgent question in the Lords, shadow Lords leader Baroness Royal warned that refusing to do so would be seen as "incomprehensible both by the public and by News Corporation's advertisers and investors".
But Baroness Rawlings, speaking on behalf of the government, said Culture Secretary Jeremy Hunt was confined to considering issues of media plurality when making his decision.
Labour are also continuing to call for Rebekah Brooks - News International chief executive and former editor of the News of the World - to resign.
On Wednesday, she received the backing of News International owner Rupert Murdoch who also said the allegations were "deplorable and unacceptable".
Mr Cameron has said "everybody at News International should ask themselves some searching questions", but he has come under personal pressure over his decision to hire another former News of the World editor, Andy Coulson, as his director of communications after he resigned from the paper in 2007 over the phone hacking scandal.
Allegations about the targeting of politicians and celebrities, including actor Hugh Grant and former Deputy Prime Minister Lord Prescott, have been known for some time.
But in recent days it has been claimed that the voicemail of murdered schoolgirl Milly Dowler was hacked by the News of the World, as well as at least one of the parents of Soham victims Holly Wells and Jessica Chapman.
It has also emerged that Chancellor George Osborne has also been informed by police that his name and home phone number had been found in notes kept by private investigator Glenn Mulcaire and the former News of the World reporter Clive Goodman.
A spokesman for the chancellor said there was no suggestion his phone had been hacked.