Witnesses said police fired tear gas into a group of demonstrators marching near Syntagma Square in central Athens to try to force the protesters to move on, the British publication The Guardian posted in a running blog about the strike.
Police confirmed one death of demonstrator although the cause of death was undetermined.
"There is some speculation that he had a fainting fit and other suggestions that he either suffered a cardiac arrest or stroke," said police spokesman Lt. Col. Christos Manouras in Athens.
Earlier, witnesses said several individuals threw objects and kicked at riot police in Syntagma Square. Soon after, the group scattered and a large group of peaceful demonstrators marched.
Teachers marching elsewhere in Athens carried signs that read: "No to the destruction of public education."
Transportation disruptions were expected throughout the country during the day as transit and transportation workers said they would halt service for much of the day, The New York Times said. Air traffic controllers also signaled they would join government and private-sector workers in the strike. The main retailers association urged shopkeepers to close their doors.
The national strike in Greece -- called as European Union leaders were meeting in Belgium -- is the latest push-back by citizens in financially troubled European countries against draconian cuts sought by leaders to help pull their economies from the brink, the Times reported.
In total, five people have died in Greece in various demonstrations since 2010. One man died of a heart attack last year while demonstrating. In May 2010, three people died during a fire at a bank that began during a demonstration, the Guardian said.
The action in Greece came as the country's trio of lenders -- the International Monetary Fund, the European Central Bank and the European Commission -- pressured Prime Minister Antonis Samaras to approve austerity cuts amounting to 13.5 billion euros (about $18 billion), including new wage and pension cuts, as well as demands to streamline labor laws seen as hurting the country's competitiveness.
The package is needed to free up a 31.5 billion euro loan (about $41.29 billion) Greece needs to stay solvent.
"Agreeing to catastrophic measures means driving society to despair," said Yannis Panagopoulos, leader of Greece's largest private-sector union. "The consequences as well as the protests will then be indefinite."
Leaders hope to agree to final details of the austerity plan in coming days, the Times said.
Spain, meanwhile, successfully conducted a debt sale Thursday, The Guardian reported, selling 4.61 billion euros (about $6.04 billion) of long-term bonds, more than its target of 4.5 billion euros (about $5.9 billion).
However, the Bank of Spain reported bad loans across the country's financial sector reached a record high in August, The Guardian said.
Financial officials said 10.5 percent of all loans held by Spanish banks were in arrears in August, up from 9.9 percent in July.