After No 10 made clear the Prime Minister was taking a "close interest" in the abuse claims, which include allegations against a senior Tory from the Thatcher era, Mr Cameron announced the new probe while on a trade mission to Abu Dhabi.
Abuse victim Steve Messham wants to meet Mr Cameron. The PM said: "These actions are truly dreadful and mustn't be left hanging in the air. I am taking action today, first of all to make sure Mr Messham can meet urgently with the Secretary of State for Wales so he can hear his allegations and his points directly.
"Secondly, I am going to be asking a senior independent figure to lead an urgent investigation into whether the original inquiry was properly constituted and properly did its job and to report urgently to the Government. But third, I would also urge anyone who knows anything about these matters to go to the police."
Downing Street signalled there may be two inquiries, one to look at the original inquiry and the second the police response at the time.
A three-year inquiry into child abuse claims at the Bryn Estyn children's home was led by Sir Ronald Waterhouse, a retired judge. Some 28 alleged abusers were identified but not named.
Peter Howarth, who was Bryn Estyn's deputy head, was jailed in 1994 for for sexually abusing teenage boys. He died in jail.