WASHINGTON (AFP) - US police are reopening old murder cases after concluding that a man shot dead with his own gun by an alleged prostitute in her home may have been a serial killer.

Neal Falls, 45, killed on July 18 in Charleston, West Virginia, may be linked to the murder or disappearance of nine women in three states, police say.

"Our victim was the tenth. But she survived," Lieutenant Steve Cooper, the lead detective in the West Virginia case, told AFP on Tuesday.

In the trunk of Falls' car, police found knives, an axe, a machete, a sledgehammer, plastic bags, bleach, a bullet-proof vest and four sets of handcuffs.

Cooper has called it "a serial killer kit."

Falls had arranged to meet with the woman via a website advertising escort services.

The woman, who has asked to be identified only as Heather, told CBS News over the weekend that as soon as Falls entered her home he pulled out a handgun, asked her if she wanted to live or die and started choking her.

"When he strangled me, he just wouldn't let me get any air and so I grabbed my rake. And when he laid the gun down to get the rake out of my hands, I shot him. I just grabbed the gun and shot behind me," she said, making the gesture of reaching behind her head and shooting blindly.

The shot hit Falls in the head, killing him.

DNA samples from Falls have been entered into an FBI database to see if they match evidence from old cases, Cooper said.

On Falls' person, police found a yellow Post-it note with the names, ages and telephone numbers of other women.

A 'LIKELY' SERIAL KILLER

Falls is now being investigated over the killings or disappearance of nine women in Nevada, Ohio and Illinois, Cooper said.

All or most of those women worked as escorts and advertised online, he said.

And one other state - Kentucky - also recently contacted authorities in West Virginia with queries, Cooper said.

He said it is likely Falls was a serial killer, given the places he was known to have lived, the items found in his car and what he tried to do to Heather.

In 2005, while he was living in Nevada and working at the Hoover Dam, four young women either went missing or were killed and dismembered. One of the sets of body parts ended up in Illinois.

"The items found in his trunk are for dismembering," Cooper told AFP. "All of that stuff would lead you to believe it is very suspicious."

The woman Heather will not be charged as the killing has been ruled an act of self-defence.

After shooting Falls, Heather says she ran outside and flagged down a neighbour, who called police for her.

"She had to defend herself and she shot him," the neighbour is heard telling an emergency police dispatcher. "She's got cuts and stuff all over her."

In the background, Heather is heard whimpering, "he pulled a gun on me. He pulled a gun on me."

And in the interview broadcast by CBS outside her home, speaking more calmly, Heather said: "I knew he was there to kill me."