Koci Selamaj, 36, travelled to London from his home in Eastbourne on the south coast to carry out what the prosecution alleges was a “pre-meditated and predatory” attack.
It is claimed he struck 28-year-old Ms Nessa with a 2ft long weapon as she walked through Cator Park in Kidbrooke, south-east London, on her way to meet a friend on September 17.
The body of Ms Nessa, who taught a year one class at Rushey Green Primary School in Catford, was found nearly 24 hours later covered with grass near a community centre in the park.
It is believed Ms Nessa’s attacker was a complete stranger to her.
Selamaj, from Eastbourne, East Sussex, was arrested in the seaside town and charged with her murder.
On Thursday, Selamaj, an Albanian national, appeared at the Old Bailey for a plea and directions hearing.
The defendant, who is in custody, entered a formal not guilty plea to murder.
But it was indicated on his behalf that he accepts responsibility for killing Ms Nessa.
Addressing defence barrister Aidan Harvey, Mr Justice Wall said: “Is there any dispute your client killed Ms Nessa?”
Mr Harvey replied: “There is not, my Lord. He accepts he killed her.”
Members of the victim’s family sat in court a few metres from the defendant, who was assisted by an Albanian interpreter, in the dock.
Bearded Selamaj, who wore a face mask and grey T-shirt, spoke only to confirm his identity and enter a not guilty plea.
Mr Justice Wall set a further hearing for February 25 next year.
He set a trial of up to five weeks from June 7.
The defendant was remanded into custody.