Police spokesman Panagiotis Papapetropoulos told The Wall Street Journal two officers were injured by masked, bottle-throwing youths, and 24 people were arrested.
Police said 20,000 people marched in Athens, while organizers reported 30,000.
Across Greece, civil servants, teachers and hospital staff walked out, and government offices, schools and universities closed down for the day. Ferry and rail transport were halted.
The government is planning to present Parliament with another $37.4 billion in budget cuts to satisfy creditors.
Britain's Daily Mail reported the government is putting marinas, casinos, former Olympic venues and vast tracts of state-owned land up for sale to pay off its huge debts.
On Tuesday, Prime Minister George Papandreou urged his Cabinet to pull together and commit to meeting the fiscal goals Greece has promised the European Union and the International Monetary Fund, the Kathimerini newspaper reported. Some ministers have been questioning his leadership.
"We are sending a message of belief in the country's powers and determination to change Greece," Papandreou after meeting with President Karolos Papoulias
Since narrowly averting default a year ago, Greece has cut its budget deficit by about a third.
Notable deaths of 2014 [PHOTOS]
Oscar Pistorius receives 5-year sentence