France and Italy and other EU countries running excessive deficits but which have scraped through an initial review of 2015 budgets may still have to do more, the European Commission said today.
A fuller assessment will show next month whether other measures are needed.
"It cannot be excluded" that the Commission may have to take further steps to ensure compliance, EU Economic Affairs Commissioner Jyrki Katainen said.
Katainen said that after talks, "some member states have changed their budgetary plans at the last minute".
"In all cases, member states have responded constructively to our concerns. That is very important and welcome," he said.
The outcome "is good news and it shows that our economic governance is working and having an impact," he added.
The budget review covered the 18 euro zone countries, with the focus on struggling France and Italy after Brussels told them that their original plans risked being rejected outright.
All 28 European Union countries are required to keep their annual budget deficits - the shortfall between revenue and spending - below 3% of Gross Domestic Product, with total accumulated debt not more than 60%.
If member states breach these rules, they can face reprimand, sanctions or ultimately fines but in practice most of them have repeatedly flouted the limits, sometimes for years.
The Commission, the EU's executive arm, gained far-reaching powers during the debt crisis to vet euro zone budget plans before they were enacted to ensure the single currency countries in the future stick strictly to the rules.
France originally forecast a 2015 deficit of 4.3% and said it would not reach the EU target until 2017.
But on Monday, French Finance Minister Michael Sapin said he had found another €3.6 billion to reduce the deficit. Italy similarly announced that it would step up efforts to tackle its structural budget deficit - the underlying shortfall left after variables are stripped out.
Additionally, it promised to do more to reduce its massive debt, put at 133.4%of GDP in 2015.
The French and Italian governments have both argued that the rules should be relaxed at a time when the European economy has stalled, undercutting efforts to cut very high jobless rates.
Growth is the priority, they say, and the rules need to be applied with the most leeway possible to allow governments to invest and get the economy going again.