On Sunday, riot police, hoping to avoid the lengthy riots of last year, fired tear gas at thousands of demonstrators as they marched through Athens and other Greek cities.
About 277 people were detained in the capital and 26 arrested, while 26 police officers, 4 people, and the dean of Athens university were injured.
Greece's government had deployed more than 6,000 police officers onto the streets of the capital to avert a repeat of last year's riots which caused millions of dollars of damage.
Sporadic scuffles between stone-throwing protesters and riot police broke out around Athens, with police in full riot gear firing tear gas to disperse small groups of hooded youths.
On Saturday, Greek police had arrested more than 150 people in Athens in an attempt to head off trouble.
Greece's government has said it will not tolerate a repeat of last year's violence. Karolos Papoulias, the president of Greece, had pleaded for calm ahead of the planned protests.
"The murder of Alexis Grigoropoulos was not only a heinous act, it was a lesson for us all ... an obligation to try and ensure a fairer society for our younger generation," he said.
Theodoros Pangalos, the Greek deputy prime minister, said: "We will not tolerate lawlessness and attacks on innocent citizens."
Grigoropoulos was shot dead by a police officer who claimed he fired into the air whilst under attack by youths.
Two police officers have been charged with murder and attempted murder for the teenager's death and are scheduled to stand trial on January 20.
Fears of violence have been heightened by reports that groups of anarchists from other European countries are planning to join the protests in Athens.