The strike, the largest such action by Chilean students in decades, is the first domestic crisis of Michelle Bachelet's nearly three-month-old government.
Public high school pupils are demanding free bus fare, free college entrance exams, more teachers, and improved secondary school buildings.
They rejected the president's offer last week of $135 million in additional annual funding for school programmes, saying it failed to meet their key demands.
"Our demands from the start have been for sweeping changes to the education system," said Maria Jesus Sanhueza, a student leader.
While there were no reported injuries, some 160 demonstrators were arrested and police said many were older than high school age.
Bachelet said reforms would be implemented with or without a strike, but she would not bend further to student demands.
"I am sorry we are experiencing this strike today, because in my view it is not necessary," she said.
The protests increased in intensity as the day progressed, with some demonstrators damaging public property, smashing downtown store windows and attacking police with rocks and other projectiles.
Police in vehicles responded with jets of water and tear gas, sending protesters and bystanders coughing and scampering.
"Our movement is peaceful but we understand that at times the malcontent of our comrades can translate into violence," Sanhueza said.
The student protests pose a test
for the popular new president
The marches were still more subdued than last week's, in which students, police and journalists were injured.
In the coastal city of Valparaiso, some 14,000 students marched peacefully through the streets, while in Santiago groups of police marched in formation behind riot shields to disperse pockets of demonstrators.
More than 600,000 students were officially involved in the strike, although they were joined by several hundred thousand sympathisers - including university students - after talks with the government broke down at the end of last week.