They, along with other public servants and hospital workers, have gone on a 48-hour strike, with a nationwide strike by public and private sector workers is expected on Wednesday.
'Message to Europe'
The action comes two days after the government announced sweeping spending cuts worth $40bn to secure a joint European Union-International Monetary Fund rescue package to help Greece out of its debt crisis.
Earlier on Tuesday, about 100 protesters from the Greek Communist Party cut through locks on the gates of the Acropolis and hung banners reading: "Peoples of Europe - Rise Up".
"This is a message to the people of Europe," Panagiotis Papageorgopoulos, a Communist party official, said.
"People have the same problems everywhere. We can take control of our fate with organised protests, so that our lives are not run by the EU and the IMF."
The new measures, which are being submitted in a draft bill to parliament on Tuesday and are to be voted on by the end of the week, will result in deeper
cuts in pensions and public servants' pay, and a new hike in consumer taxes.
While Tuesday's strike saw a number of flights cancelled, Wednesday's strike is expected to shut down services across the country.
Public transport will halt in the morning and evening, government offices will remain closed throughout the day and state hospitals will function with emergency staff.
The Athens Traders Association said it was recommending that stores in the capital remain open during the strike, but shut down during demonstrations planned in the centre as a show of solidarity for the strikers.
Around 300 pensioners also held their own demonstration on Tuesday, marching through central Athens to protest pension cuts and consumer tax hikes, chanting
"Stealing our pensions is not the answer".
"We won't let them steal our livelihoods, they are cheating us," Dimos Koumbouris, head of a pensioners' union, said.
"Tomorrow everything will close, factories, shops, everything - they will hear our voice very clearly."
With a budget deficit of 13.6 percent of gross domestic product, Greece has been struggling to pull its finances in order and was less than three weeks away from default when the eurozone finance ministers agreed to activate the three-year $146bn rescue package.