The killing of Grigoropoulos has sparked the worst rioting Greece has seen in decades, with at least 70 people injured in cities across the country.
Hundreds of stores have been smashed and looted, and more than 200 people have been arrested.
Earlier, hundreds of schoolchildren holding candles gathered peacefully outside the parliament building in Athens and at the site where Grigoropoulos was shot.
They left candles spelling out the name "Alex" in front of a line of riot policemen.
Banners in the main square outside parliament read: "The state kills" and "Down with the government of murderers".
"The murder of Alexis was the last straw. Being a young man in Greece today is a crime ... They are stealing our dreams," said one leaflet distributed in the square.
The young protesters promised to remain on the streets until their concerns, including opposition to the increasingly unpopular government and worry over economic issues, are addressed.
Throughout most of the day, the capital had appeared calmer than in the past week.
Christmas shoppers cautiously returned to central Athens earlier on Saturday, but many stores had boarded up their windows instead of replacing the glass, for fear of further violence.
Much of the rioting has been blamed on an anarchist fringe tapping into resentment over political scandals and the impact of the global slowdown.