Margaret Anderson, a park ranger, was shot dead late on Sunday by the suspect [AFP]

US police have confirmed that a body found in Mount Rainier National Park near Seattle, Washington is the man wanted in the shooting death of a park ranger.

A plane searching the park for the suspect found the body lying face down in chest-deep snow on Monday.

The suspect, Benjamin Colton Barnes, 24, is believed to have fled to the remote park to hide after an earlier shooting at a house party near Seattle that wounded four, two critically.

Authorities suspect he shot ranger Margaret Anderson later on Sunday.

Police cleared out the park of visitors and mounted a manhunt for Barnes, an Iraq war veteran.

At Mount Rainier, Barnes had allegedly sped past a checkpoint. While one ranger began following him, Anderson eventually blocked the road to try stop him. Before fleeing, Barnes allegedly fired shots at both Anderson and the ranger who trailed him, but only Anderson was hit.

'I want to die'

Barnes has had a troubled transition to civilian life, with accusations he suffers post-traumatic stress disorder and is suicidal.

He was involved in a custody dispute in July, during which his toddler daughter's mother sought a temporary restraining order against him, according to court documents.

The woman told authorities he was suicidal and possibly suffered from post-traumatic stress disorder after deploying to Iraq in 2007-2008, and had once sent her a text message saying "I want to die."

She alleged that he gets easily irritated, angry and depressed and keeps an arsenal of weapons in his home. She wrote that she feared for the child's safety.

Undated photos provided by police showed a shirtless, tattooed Barnes brandishing two large weapons.

The shooting renewed debate about a federal law that made it legal for people to take loaded weapons into Mount Rainier. The 2010 law made possession of firearms in national parks subject to state gun laws.