Benjamin Colton Barnes, 24, apparently died after trudging into chest-deep snow in the Washington state park while trying to elude SWAT team members and other police who were on his trail.
Mr Barnes reportedly fled to remote Mount Rainier National Park following an earlier shooting in a house near Seattle that left four people injured.
Washington State Patrol spokesman Guy Gill said a body believed to be Barnes was found face down in the snow. His identity has not been confirmed.
The park had been evacuated following the killing of ranger Margaret Anderson, who was shot dead on Sunday.
The park remained closed yesterday as police hunted for Barnes. About 150 officers were involved in the search.
Pierce County Sheriff’s spokesman Ed Troyer said that Mr Barnes, an Iraq War veteran believed to have survivalist skills, was a “strong person of interest” in the ranger’s death.
Authorities believed the gunman was still armed as they continued their search.
It has been legal for people to take loaded firearms into Mount Rainier and other national parks since 2010.
Parks spokesman Kevin Bacher said: “The speculation is he threw some stuff in the car and headed up here to hide out [after the Seattle shooting].”
Officials used the cover of morning darkness to lead about 125 tourists out of the park to safety after they had been temporarily held at a visitor centre while the hunt unfolded.
Dinh Jackson, from Olympia, Washington, who came to the mountain park to sledge with family and friends, said officials ordered people to hurry into the lodge after the shooting.
Ms Jackson said officials had everyone get on their knees and place their hands behind their heads in the lodge as staff went through the building, looking at faces to make sure the gunman was not among them.
A parks spokesman said Mr Barnes had served in the military, and the mother of his child had alleged he suffered from post-traumatic stress following his deployments.
Mr Barnes was involved in a custody dispute in the town of Tacoma in July last year, during which the toddler’s mother sought a temporary restraining order against him, according to court documents.
In an affidavit, she wrote that Mr Barnes was suicidal and possibly suffered from PTSD after deploying to Iraq in 2007-8. She said he got easily irritated, angry and depressed and keeps an arsenal of weapons in his home.
Mr Barnes is a suspect in a shooting early on Sunday that left four people injured, two critically, at a house party south of Seattle, police said.
At Mount Rainier on Sunday morning, Mr Bacher said the gunman had sped past a checkpoint set up to make sure vehicles have tyre chains, which are sometimes necessary in snowy conditions. One ranger began following him while Ms Anderson, 34, a mother of two young children, blocked the road to stop the driver.
Before fleeing, the gunman fired at both rangers, but only Ms Anderson was hit. Mr Troyer said she was shot before she had even left the vehicle.
Authorities have recovered Mr Barnes’s vehicle, which contained weapons and body armour.
There was some anger at the change in the law, in 2010, which allowed people to be armed in some national parks.
Bill Wade, the outgoing chairman of the Coalition of National Park Service Retirees, called the shooting a tragedy that could have been prevented.