The report, commissioned after Japan's Fukushima nuclear disaster, aimed to see how Europe's nuclear power stations would cope during extreme emergencies.
The final report is to be published on Thursday. The draft says nearly all the EU's 143 nuclear plants need improving.
Anti-nuclear groups say the report's warnings do not go far enough.
For its part, the regulatory body for European nuclear safety has urged the Commission not to use language that could undermine public confidence, says the BBC's Chris Morris in Brussels.
The report - the wording of which could change before Thursday's final version is published - points out that in the EU, 47 nuclear power plants with 111 reactors have more than 100,000 inhabitants living within a circle of 30km.
"On the basis of the stress test results practically all [nuclear plants] need to undergo safety improvements," says the leaked draft. "Hundreds of technical upgrade measures have already been identified.
"Following the accidents at Three Mile Island and Chernobyl, urgent measures to protect nuclear plants were agreed. The stress tests demonstrated that even today, decades later, their implementation is still pending in some member states."
Four reactors in two unnamed countries would have less than an hour to restore safety functions if electrical power was lost, it adds.
In France, Europe's largest nuclear power producer which relies on 58 nuclear reactors for 80% of its electricity, specific failings were found in all 58 nuclear reactors.
Earlier this month, a blast of escaping steam burned two people at the Fessenheim power station in eastern France - one of the country's oldest nuclear reactors which has long been the target of regular anti-nuclear protests.
Fessenheim, close to France's borders with Germany and Switzerland, opened in 1977 and draws water for cooling from the Rhine, but campaigners say its location makes it vulnerable to seismic activity and flooding.
Shortcomings were also reported in the UK. Most of the country's power plants lacked an alternative emergency control room to use if the main one became contaminated by high radiation, says the report.
The UK's Department of Energy said there was no evidence UK nuclear facilities were unsafe.
"However, the Government is committed to the principle of continuous improvement," a spokesman told the BBC.
"We are working closely with the Office for Nuclear Regulation to ensure that operators address any site specific issues using the existing robust UK regulatory regime, which requires operators to take all reasonably practicable steps to reduce risk and seek continuous improvements to safety."
Call for closures
While the stress tests found deficiencies in many of Europe's nuclear reactors, campaigners say they failed to address risks in crucial areas, such as ageing technology, terrorist attacks or human error.
"If this exercise was serious, the Commission should be recommending the closure of unsafe or ageing reactors," said Rebecca Harms, co-president of the Greens/European Free Alliance at the European Parliament.
"At the very least, the Commission should be pressing for the security deficiencies identified in the report to be rectified."
As of June, all 143 nuclear plants in the EU were to be re-assessed using criteria covering both natural and man-made hazards.
Some governments have reappraised their nuclear energy strategy in the aftermath of last year's Fukushima disaster, with Germany deciding to abandon nuclear energy for green technology and cleaner gas- and coal-powered plants by 2022.
Others, like France, have boosted investment in nuclear power since the meltdown.
The Fukushima Daiichi nuclear plant's cooling systems were knocked out by the 11 March 2011 earthquake and tsunami in Japan. The disaster caused a meltdown at three of the reactors.
[link to http://www.bbc.co.uk]