British Prime Minister David Cameron on Monday called for an emergency session of Parliament to brief members on the spreading phone hacking scandal, trying to gain control of a crisis that is threatening Rupert Murdoch’s media empire, the upper echelons of London’s police force and the country’s leader himself.

Parliament is due to break for the summer on Tuesday after MPs grill Mr. Rupert Murdoch, his son James and his former British chief executive Rebekah Brooks about the scandal, but Mr. Cameron said “it may well be right to have Parliament meet on Wednesday so I can make a further statement.”

Mr. Cameron was speaking in Pretoria, South Africa, on the first day of a two-day visit to the continent. He had planned a longer trip, but cut it short as his government faces a growing number of questions about its relationship with the Murdoch empire and a scandal that has taken down some of Britain’s most powerful people with breathless speed.

In the latest twist in the legal saga, Britain’s Serious Fraud Office, Britain’s anti-fraud agency, said on Monday it was giving “full consideration” to a request from a legislator that it open an investigation into Mr. Rupert Murdoch’s News Corp.

The office said any possible probe would be limited to News Corp. activities in Britain, but it added that it is ready to assist authorities in the U.S., where the FBI has already opened an inquiry into whether 9/11 victims or their families were also hacking targets of News Corp. journalists.

Mr. Cameron insisted his government had “taken very decisive action” by setting up a judge-led inquiry into wrongdoing at the newspaper and relations between politicians, the media and police.

“We have helped to ensure a large and properly resourced police investigation that can get to the bottom of what happened, and wrongdoing, and we have pretty much demonstrated complete transparency in terms of media contact,” Mr. Cameron said.

But he is under pressure after the resignation of London police chief Paul Stephenson and the arrest on Sunday of Mr. Rupert Murdoch’s former British CEO — and Mr. Cameron’s friend — Ms. Brooks on suspicion of hacking and police bribery.

Ms. Brooks was detained and questioned for nine hours on Sunday before being released on bail. On Monday, her lawyer released a defiant statement professing her innocence and claiming police face serious questions about her arrest. He said police would “have to give an account of their actions” considering “the enormous repetitional damage” Ms. Brooks’ arrest had caused to the ultimate social and political insider.

Mr. Stephenson resigned Sunday over his ties to a former News of the World executive editor who has been arrested over the scandal. In his resignation speech Mr. Stephenson made pointed reference to Mr. Cameron’s hiring of Andy Coulson, a former editor of the shuttered tabloid who was arrested earlier this month over hacking.

Mr. Cameron said the situations of the government and the police were “completely different,” because allegations of police corruption “have had a direct bearing on public confidence into the police inquiry into the News of the World and indeed into the police themselves.”

Other senior police officers are under fire, including Assistant Commissioner John Yates.

Ms. Brooks’ arrest was the latest blow for Mr. Rupert Murdoch, the once all-powerful figure courted by British politicians of all stripes. Now Mr. Rupert Murdoch is struggling to tame the scandal, which has already destroyed News of the World, cost the jobs of Ms. Brooks and Wall Street Journal publisher Les Hinton and sunk the media baron’s dream of taking full control of a lucrative satellite broadcaster, British Sky Broadcasting.

Mr. Rupert Murdoch is eager to stop the crisis from spreading to the United States, where many of his most lucrative assets — including the Fox TV network, 20th Century Fox film studio, The Wall Street Journal and the New York Post — are based. Sky News reported on Monday that News Corp. had appointed senior lawyer to head internal probe on phone hacking.

Ms. Brooks’ arrest had thrown into doubt her appearance on Tuesday before the committee that also will quiz Mr. Rupert Murdoch and Mr. James Murdoch. But her spokesman, David Wilson, said on Monday she planned to attend.

She was the defiant chief executive of News International, Mr. Rupert Murdoch’s British newspaper arm, whose News of the World stands accused of hacking into the phones of celebrities, politicians, other journalists and even murder victims. But, the revelation that journalists accessed the phone of Milly Dowler in search of scoops while police were looking for the missing 13-year-old fuelled an explosion of interest in the long-simmering scandal.

At an appearance before U.K. legislators in 2003, Ms. Brooks admitted that News International had paid police for information. That admission of possible illegal activity went largely unchallenged at the time and legislators are keen to ask her about it again. But she always said she did not know any phone hacking was going on when she was editor of News of the World between 2000 and 2003.

Police have already arrested 10 people, including other former News of the World reporters and editors. No one has yet been charged.

Even more senior figures could face arrest, including Mr. James Murdoch, chairman of BSkyB and chief executive of his father’s European and Asian operations. Mr. James Murdoch did not directly oversee the News of the World, but he approved payments to some of the paper’s most prominent hacking victims, including £700,000 pounds ($1.1 million) to Professional Footballers’ Association chief Gordon Taylor.

Mr. James Murdoch said last week that he “did not have a complete picture” when he approved the payouts.

Mr. Hinton, too, could face questioning over wrongdoing at the News of the World during his 12 years as executive chairman of News International. But Mr. Hinton is an American citizen living in the U.S., so British authorities would have to seek his extradition if he refused to come willingly.

Police are under pressure to explain why their original hacking investigation several years ago failed to find enough evidence to prosecute anyone other than News of the World royal reporter Clive Goodman and private investigator Glenn Mulcaire. Detectives reopened the investigation earlier this year and now say they have the names of 3,700 potential victims.

Mr. Cameron’s office said he will be back in Britain on Wednesday after visits to South Africa and Nigeria. He had also planned to visit Rwanda and Sudan but a decision was made last week to drop that part of the itinerary.

He defended his decision to make the trip despite the hacking crisis.

“Just because you’re traveling to Africa doesn’t mean you suddenly lose contact with your office,” he said.

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