Greek police warned people to stay away from central Athens on Thursday as thousands of students staged new protests over the police killing of a teenager.

Tensions were raised after the 16-year son of a Greek teacher's union official was wounded in a rifle attack on Wednesday night in an Athens suburb.

After almost two weeks of unrest and protests over the fatal police shooting of 15-year-old Alexis Grigoropoulos, police quickly denied any involvement in the new incident.

The youth was hit in the hand by a rifle bullet as he talked with other students in the street near his school in Peristeri, according to police.

The youth spent the night in hospital and underwent an operation on Thursday, police said. The Greek government promised a detailed inquiry into the shooting.

The victim was the son of a leading official in the Greek Teachers Federation which backed the latest demonstrations in Athens.

About 3000 students and teachers gathered in Athens and with other rallies held in other cities, authorities took widespread precautions to avoid a repeat of the riots and looting of the past two weeks.

Police cleared streets around the centre of the capital and told residents not to venture out during the demonstrations. Hundreds of police were on duty.

One rally, called by the Greek Communist Party (KKK) started in Omonia square and went to the Greek parliament without incident.

The main rally by students and teachers was in front of Athens University and was also to head to parliament, the scene of many of the protests over the death of Grigoropoulos.

Banners at the rally read "Mourning Is Not Enough, The Struggle Goes on".

Planned strikes and protests organised by a public employees' union over the Greek budget and anti-racism demonstrations were expected to add to the turmoil.

Rallies were also held in the second city of Thessaloniki and planned in Patras in the south and Preveza in the west.

Protest organisers called for demonstrations across Europe in solidarity. About 50 activists hung banners along the Acropolis monument on Wednesday.

One banner called for demonstrations across Europe and a second proclaimed "Resistance" in several languages.

Students claim some 600 schools and universities are occupied throughout the country. The education ministry says the figure is closer to 100.

A ballistics report on the death of Grigoropoulos was handed over to an investigating judge on Thursday, a court source said.

The judge has summoned lawyers for the police officer charged over the killing and the victim's family to inform them of the report's conclusions, the source said.

Preliminary conclusions by medical examiners and experts working for the victim's family indicated that a bullet ricocheted and hit the teenager.

Damage to the bullet showed that it had touched a hard surface before hitting Grigoropoulos in the chest, judicial sources and the police officer's lawyer said.

The officer, Epaminondas Korkoneas (37), says he was trying to defend himself from youths and killed the boy by accident when he fired three shots.

His partner, Vassilios Saraliotis (31), was charged with being an accomplice.

AFP