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The BBC's Jon Sopel: "The overwhelming smell is one of tear gas"
Thousands of protesters have gathered outside parliament in Athens and public transport in the capital has largely ground to a halt.
The rally started peacefully, but small groups of protesters later clashed with police, who used tear gas.
PM George Papandreou has said that only his 28bn-euro (£25bn) austerity plan would get Greece back on its feet.
If the government fails to win support for the austerity measures, the EU and IMF could withhold 12bn euros of loans and Greece could run out of money in weeks.
The general strike has halted most public services, banks are closed and hospitals are operating on skeleton staff.
Limited clashes have broken out between riot police and protesters on the fringes of the largely peaceful rally in the central Syntagma Square, with police firing tear gas to keep protesters back. Small fires appear to have been started by the protesters.
Some protesters have started throwing stones and bottles at the police in one corner of the square, TV images show.
Airports are shutting for hours at a time, with air traffic controllers walking out between 0800 and 1200 (0500-0900 GMT) and 1800 and 2200 (1500-1900 GMT). A number of flights were also cancelled at Athens international airport.
What went wrong in Greece?
- Greece's economic reforms, which led to it abandoning the drachma as its currency in favour of the euro in 2002, made it easier for the country to borrow money.
In Athens, the metro is the only form of public transport which will work "so as to allow Athenians to join the planned protests in the capital", metro drivers said.
More than 5,000 police officers were due to be deployed in the centre of Athens as the protesters marched towards parliament.
Protesters have blockaded the port of Pireus, near Athens, which links most Greek islands with the mainland.
"The situation that the workers are undergoing is tragic and we are near poverty levels," said Spyros Linardopoulos, a protester with the PAME union at the blockade.
"The government has declared war and to this war we will answer back with war."
The unions are angry that the government's austerity programme will impose taxes on those earning the minimum wage, following months of other cuts which have seen unemployment rise to more than 16%.
At the scene: 
From the middle of the morning, they began to march into the city centre, thousands of unionists who think spending cuts and tax rises are just too severe.
It was good-natured at first, but there is real anger bubbling beneath the surface.
Small groups of protesters dressed in black began clashing with riot police. Tear gas and stun grenades were used, and Molotov cocktails have been thrown.
Running battles have been breaking out in the streets around parliament.
It was good-natured at first, but there is real anger bubbling beneath the surface.
Small groups of protesters dressed in black began clashing with riot police. Tear gas and stun grenades were used, and Molotov cocktails have been thrown.
Running battles have been breaking out in the streets around parliament.
Some protesters have said they will encircle the parliament building to prevent MPs from entering. The austerity package and implementation law must be passed in separate votes on Wednesday and Thursday.
Polls suggest that between 70% and 80% of Greek people oppose the austerity plan."We're opposed to what they're trying to do to us," said bank worker Kali Patouna. "We know very well that these measures will be our tombstone. They will have extreme consequences for workers and for everyone on all social levels."
If the measures are passed, the next instalment of Greece's 110bn-euro bail-out will be released by the European Union and International Monetary Fund.
European officials will also start to finalise the details of a second bail-out - worth an estimated 120bn euros - designed to help Greece pay its debts until the end of 2014.
The BBC's Chris Morris in Athens says defeat for the government this week would send ripples of anxiety right across the eurozone, with Greece facing the prospect next month of becoming the first member state to default on its debts.
Greece: Crucial dates
- June 29: Greek parliament to vote on a new austerity package
- July 3: Eurozone deadline. EU will sign off latest bail-out payment to Greece - 12bn euros - if austerity package has passed
- July 15: Default deadline: Without the 12bn euros it needs to make debt repayments, Greece will default
Mr Papandreou has warned that failure to secure the new loans would mean that national coffers could be empty within days.
The new Finance Minister, Evangelos Venizelos, acknowledged that the cuts were "unfair", but said they were absolutely necessary.
But the main opposition leader, Antonis Samaras of the New Democracy party, said the thinking behind the austerity package was flawed and that tax rates should be lowered rather than raised in order to stimulate the economy.
The outcome of the debate is uncertain. Mr Papandreou faces opposition from within the governing Panhellenic Socialist Movement (Pasok), with two MPs saying they may oppose the bill.
The party has a slim majority, with 155 seats out of 300 in parliament.
BBC News
