"We are all responsible so that it does not take the step into the void," the president said in a statement.

It followed a day of violence during which protesters set fire to a bank, killing three employees.

Greece's government has vowed to pursue the spending cuts - a condition of its EUR110 billion bail-out.

The euro hit a fresh 13-month low against the dollar and European stock markets were also hit, amid concerns over Greek bail-out plans.

There are also fears Greece's debt crisis could spread to other countries.

The austerity measures - which the Greek parliament is due to vote by the end of the week - include wage freezes, pension cuts and tax rises. They aim to achieve fresh budget cuts of EUR30 billion over three years, with the goal of cutting Greece's public deficit to less than 3% of GDP by 2014. It currently stands at 13.6%.

The general strike is the third to hit Greece in as many months. The protest became violent, with petrol bombs thrown at police who responded with pepper spray and tear gas.

The bodies of two women - one pregnant - and a man were found inside the Marfin bank branch on Stadiou Avenue in central Athens. They were among 20 people working there when the petrol bomb was thrown.

Most of the employees managed to escape the fumes as the flames took hold, but the three found their way blocked as they tried to escape to the roof and they suffocated.

Prime Minister George Papandreou told MPs in parliament the killings were a "murderous act".