The European Commission, the European Union's executive arm, has warned Spain and Italy that their draft budgets for 2014 may not comply with new debt and deficit rules.
It also said French and Dutch plans only just passed muster.
Non-complying countries may have to revise their tax and spending plans before re-submitting them to national parliaments.
It is the first time the Commission has done this.
Under EU rules, eurozone member states are obliged to cut deficits until they achieve a balanced budget. They also have to reduce public debt levels.
The Commission gives countries some flexibility if their deficit is below the EU ceiling of 3% of gross domestic product (GDP) and their debt levels are falling.
But when Italy, the eurozone's third largest economy, asked for such leniency over its 2014 budget plans, the Commission refused because its public debt was still rising.
France, whose economy shrank in the third quarter, has taken steps to cut its deficit to below the 3% threshold, but its structural reform plans were only making "limited progress", the Commission said.
The country had "no margin" for error in reducing its public deficit, the executive warned.
Spain's draft 2014 spending plans were "at risk of non-compliance", said the Commission, as the country does not envisage returning to EU financial norms until 2016 at the earliest.
Other countries at risk of breaking EU finance rules included Finland, Luxembourg and Malta.
The countries coming under the Commission's "budgetary surveillance" are: Austria, Belgium, Croatia, Estonia, Finland, France, Germany, Italy, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Slovakia, Slovenia, and Spain.
Those heavily indebted countries that received EU bail-outs at the height of the financial crisis - Ireland, Cyprus, Portugal and Greece - were not included in the review.
On Thursday, official figures showed that the eurozone economy grew by just 0.1% in the July-to-September period, down from 0.3% growth in the previous quarter.
The European Central Bank (ECB) last week cut its benchmark interest rate to 0.25% in an attempt to give some impetus to the fragile recovery.
Meanwhile, the annual rate of inflation across the eurozone fell to 0.7% in October, the lowest level for four years in the 17-country currency area, the EU's statistics agency Eurostat said, confirming an earlier estimate.
This compared to a rate of 1.1% in September. The ECB's target rate is just under 2%.
The October figures revealed a sharp divergence between countries, with Germany's 1.2% contrasting with Spain's 0%.