EU finance ministers have agreed new rules that will automatically punish EU states that break budgetary rules.
The plan, proposed by the European Commission, would punish countries that fail to bring their debts under control, posing a threat to the euro.
The proposals include automatic fines for countries that do not manage their finances or their economies properly.
However, governments would be given six months to bring their deficits within the 3% limit before incurring a fine.
"A country with excessive deficits which does not take the necessary correction measures within six months will be sanctioned," said French President Nicolas Sarkozy.
The French government had previously expressed reservations about the idea of automatic fines, and Poland and Italy also had strong objections.
But they appear to have given way to pressure from Germany over this point, having won the concession of a six-month cure period.
The proposed new rules aim to prevent a repeat of this summer's debt crisis when the eurozone stepped in to bail out the debt-laden Greek government.
An even bigger package then had to be put together to stop the debt crisis spreading to other countries, such as Ireland, Portugal and Spain.
Mr Sarkozy said that the French and Germans also want to introduce a permanent bail-out facility for Eurozone countries, before the current one expires in 2013.
He said doing this would require an amendment the Lisbon Treaty, although it is unclear whether this amendment would entail full ratification by all 27 EU members.
The new rules will require national governments not only to keep their deficits within the current limit of 3% of GDP, but also to actively reduce their total debt towards 60% of GDP.
Governments would be expected to cut one-20th of the excess debt every year.
So for example, a country with 100% debt-to-GDP ratio would be expected to cut it by 2% a year.
Most eurozone members are in breach of the 60% limit. Belgium, Italy and Greece have debt close to or in excess of 100% of their GDP.
And nearly all eurozone governments are currently in breach of the 3% deficit rule, as they struggle to cope with high unemployment and dismal growth.
However, there is expected to be a three-year grace period for governments to meet the financial rules.
Under the old rules, if a government could have been fined for breaching the 3% deficit limit if a majority of EU members voted to do so.
In practice this never happened, particularly as Germany and France both fell foul of the rule.
Under the new "automatic" sanctions, governments would have to keep cash equal to the fine in a bank account.
If they breach the 3% limit - and fail to come back inside the limit within six months - they would lose the money unless a majority of EU governments voted to waive the fine.