Labour leader Ed Miliband has insisted that simply reopening the paper as "the Sunday Sun" would not be enough to answer critics.
Reiterating his demand for News International chief executive Rebekah Brooks, who was editor when Milly Dowler's phone was allegedly hacked, to consider her position, he said: "I welcome James Murdoch's admission of serious errors. But closing the News of the World, possibly to reopen as the Sunday Sun, is not the answer.
"Instead those who were in charge must take responsibility for what happened. And politicians cannot be silent about it."
The Labour leader also called for the press watchdog to be scrapped in the wake of the phone-hacking scandal, saying it had been exposed as a "toothless poodle".
He backed continued self-regulation of the press, but said the Press Complaints Commission (PCC) had "totally failed" to get to the bottom of the phone-hacking allegations.
"Its chair admits she was lied to but could do nothing about it. The PCC was established to be a watchdog, but it has been exposed as a toothless poodle," he said. "Wherever blame lies for this, the PCC cannot restore trust in self-regulation. It is time to put the PCC out of its misery."
He called for Fleet Street figures to lead reform themselves and help create a new body with more independence from newspapers, tougher investigative powers and the ability to force corrections.
"Change should be led by the many decent editors and people in the industry who want to see change," he said.
"I call on journalists, and those concerned with decent journalism, to put the reform of the system of self-regulation at the centre of their concerns."
He added: "The press would be showing to the public that it was taking the first steps to cleaning up its act if it started to make change now. Today, I want to call on all the many decent people in the industry to take the initiative and start to make this happen."
