It is understood the Oscar-winning director approached immigration officials himself to ask if Mr Echols could be allowed in for a short period as his guest.
Because his murder convictions still stand, he needed a special direction - a form of character waiver - from Immigration NZ or its associate minister to be allowed entry.
Normally, anyone convicted of murder would be considered an excluded person under section 15 of the Immigration Act 2009.
Sir Peter's approach is believed to have been the catalyst for Mr Echols' visa being granted.
There has been speculation in United States media that Mr Echols has been given a small role in The Hobbit, which is in production in Wellington.
However, it is believed he has not been issued with a work visa so is not legally allowed to work while here.
Despite the guilty pleas of Mr Echols and his co-accused, the state allowed them to maintain their innocence while recognising prosecutors probably had enough evidence for conviction.
They also had to give up their right to seek compensation for a miscarriage of justice.
They were convicted in 1994 of killing Cub Scouts Steve Branch, Christopher Byers and Michael Moore, whose bodies were found in a West Memphis ditch naked, bound and mutilated.
Last year, Sir Peter denied he was making a film about the West Memphis Three. But a source said he was possibly considering making a documentary about the case and that was the reason for Mr Echols' visit.
