Parents of slain jogger Karina Vetrano offer killer reward money

The grief-stricken parents of one of the three female joggers killed in America over the last two weeks have issued a call to justice, urging their daughter's killer to come forward and even offering him reward money.

Phil and Cathy Vetrano, whose daughter Karina Vetrano was brutally murdered while out jogging in broad daylight on August 2, offered an undisclosed sum of money raised privately so far to the unknown killer, to be given to the person of his choice, NBC News reports.

"Turn yourself in. I will make sure that reward money goes to the person of your choice. The sister, your mother, your brother. It's a life-changer," Mr Vetrano, a retired firefighter, said. "You will be caught, so take advantage of that."

The victim's mother, Mrs Vetrano added: "We will get you. It's just a matter of time."

She pleaded with the public: "Don't protect him. He's of no use to anyone. He's a weak, evil piece of sh*t."

Karina Vetrano, 30, was killed after going for a solo run near her home in Howard Beach, an upscale neighbourhood in Queens, at 5pm.

Police say she was dragged off the jogging path in an area of parkland dominated by weeds and marshes. She was sexually assaulted and strangled.

The killing of a beautiful young woman during the day in an affluent part of the city has rocked New Yorkers accustomed to historically low crime rates.

The Vetrano family's offer came as more than 1000 people turned out for a memorial walk at the Queens park on Tuesday night, where their daughter was found dead two weeks earlier.

Carrying white balloons in her honour, Mrs Vetrano led the crowd of supporters and said the fact that so many people showed up to pay tribute is "evidence to everyone the power that my daughter has."

Last week, the family started a GoFundMe page to gather money for a reward leading to an arrest in the case. More than $US245,000 has been raised so far, exceeding their initial goal of $100,000.

Five days after Ms Vetrano's murder, another female jogger was killed while going for an afternoon run. Vanessa Marcotte, a 27-year-old Google executive from New York, was found dead near her mother's home in Princeton, Massachusetts, on August 7. Her body was discovered just after 8pm in a wooded area without clothes and had burns on her head, feet and hands.

No arrests have been made in either case.

Prior to both of these murders, 31-year-old Alexandra "Ally" Brueger was shot four times in the back and killed while running in Michigan on July 30.

Michigan State Police is now offering a $US5,000 reward for the arrest and conviction of the person responsible for the murder of the registered nurse and writer.

Since the weekend, Ms Brueger's picture has started appearing alongside those of Ms Vetrano and Ms Marcotte in the US press as speculation grows that all three deaths may have been targeted by a serial or copycat killer.

Police have said it is too early to rule out a possible connection regarding the homicides of Ms Vetrano and Ms Marcotte, but have not yet commented about a possible connection to Ms Brueger's case.

The murders have prompted community women's running groups in New York, Princeton and Rose Township to start their own safety campaigns.

Women were now too frightened to jog alone, The New York Times reported.