The National Rifle Association (NRA) has joined other US gun lobby groups in calling for a "full investigation" by the Trump administration into the killing of Alex Pretti in Minnesota.

Comments from the NRA come after a border agent fatally shot Pretti - registered nurse at a Veterans Affairs hospital - in Minneapolis on Saturday.

State and federal officials have given starkly different accounts. The Trump administration has said Pretti carried a gun and posed a danger to officers - while no available video shows Pretti holding a gun.

The NRA labelled a suggestion by a federal prosecutor that people who carry guns risk being lawfully shot by officers as "dangerous and wrong".

"Responsible public voices should be awaiting a full investigation, not making generalisations and demonising law-abiding citizens," the NRA said in a statement.