The country currently has a spiralling public deficit of 12.7%, more than four times higher than eurozone rules allow.
The government has pledged to cut this to 8.7% this year, and also reduce the 300bn-euro ($419bn; £259bn) national debt, by freezing public sector salaries, raising the average retirement age to 63 by 2015, and increasing taxes on petrol, alcohol and tobacco.
It also wants to crack down on tax avoidance. Greece's black economy is estimated at 30% of official gross domestic product.
The BBC's Malcolm Brabant in Athens says that for the second time this month, Greece is isolated from the rest of the world for 24 hours as all flights into and out of the country have been cancelled.
Commuters have been left without most forms of public transport, while public schools, ministries, and municipal offices have been closed. Many hospitals are operating only with emergency staffing.
Today, from all locations in the country, a strong message of unity, struggle and protest is being sent
Yiannis Panagopoulos Head of GSEE private sector union
Demonstrations were held in Athens and Thessaloniki.
Our correspondent, who was at a protest in the centre of the capital that police estimated was attended by 25,000 people, said the mood there was resolute.
The march was peaceful but scuffles broke out between some demonstrators and police as the rally came to an end, and tear gas was fired.
Groups of youths then threw stones and smashed shop windows, police said. Three people were arrested.
The brief clashes were a distraction from the union's main message that Greece's rich should pay for the crisis, not the working and middle classes, our correspondent says.
The march was three times bigger than one held two weeks ago during the last 24-hour stoppage, our correspondent adds, but given that two million people were supposedly on strike, it was hardly the start of a revolution.
The country's two largest trade union groups, the private sector GSEE and the public sector ADEDY, had predicted a substantial turnout among their two million members.
"Today, from all locations in the country, a strong message of unity, struggle and protest is being sent," the head of the GSEE, Yiannis Panagopoulos said in a statement .
"Today Greece is the guinea pig for EU stability and the euro's resilience. Today it is Greece, tomorrow it will be Spain, Portugal and Italy."
Mr Panagopoulos said the government should adopt a mix of economic and social policies that would not lead to recession, but create jobs.
Deputy Prime Minister Theodoros Pangalos told the BBC the government was not worried by the strike and would press ahead with the economic plan.
"What we have faced up until now and, I think, what we are going to face in the next days to come, are very mild. This is shown also by polls, which give overwhelming support to this government," he said.
Mr Pangalos also made a strident attack on the calibre of the EU's current political leaders, saying those of the 1980s - such as Margaret Thatcher, Helmut Kohl and Francois Mitterrand - would never have permitted the current economic crisis.
Athens police estimated that 25,000 people marched in the capital
"This is another level of leadership which we don't have today. The quality of leadership today in the union is very, very poor indeed," he said.
Although the EU has offered moral support to Greece, it has been far from enthusiastic, not least because of the country's dubious accounting practices, our correspondent says.
But Mr Pangalos accused Italy of being more inaccurate with its financial statistics, and said Germany should not criticise Athens because it had wrecked the Greek economy and slaughtered thousands during the Nazi occupation.
"They took away the gold that was in the Bank of Greece, they took away Greek money, and they never gave it back. This is an issue that has to be faced sometime in the future," he added.
More than 300,000 Greek civilians died from starvation during World War II, while thousands more were killed in reprisals. The economy was crippled, as foreign trade was suspended, agricultural output ground to a halt, and the treasury had to lend Germany money.
Germany paid Greece about 115m Deutschemarks in 1960 to compensate victims of Nazi persecution, but it has refused more recent demands for further funds. However, some Greeks say the compensation did not cover civilian victims of reprisals and the loan.
Analysts say Greece may be forced to implement even tougher austerity measures to meet EU demands in the coming months. This could include a rise in value-added tax (VAT), which stands at 19%.
On Tuesday, the credit ratings of Greece's four largest banks were downgraded by ratings agency Fitch, a move that may worsen the country's financial woes.
The move will make it more expensive for the banks to borrow funds, and the government to get loans.
Greece is required to report back to fellow eurozone nations by 16 March on how well its efforts are progressing.
Finance ministers from the other 15 nations that share the single currency have warned that the Greek government may have to adopt further measures if the ones currently being enforced are not shown to be working fast enough.
At the weekend, Prime Minister George Papandreou told the BBC that Greece was not looking for a financial bail-out from other European countries.
He said that Greece was instead looking for political support from across Europe to enable it to borrow money at the same interest rates as other countries.
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