An EFSA task force set up to track the possible source of the disease said it recommended in consequence that "all efforts be made to prevent any consumer exposure to the suspect seeds."
In a statement, EFSA said "that one lot of fenugreek seeds imported from Egypt and used to produce sprouts is the most likely common link between the two outbreaks" - referring to the German outbreak and another, relatively minor outbreak of a different E. coli strain in France.
"However, it cannot be excluded that other lots of fenugreek imported from Egypt during the period 2009-2011 may be implicated," it added.
After the release of the report the European Union on Tuesday banned Egyptian fenugreek seeds and slapped a temporary ban on the import of all seeds and beans from the country.
"The report published today leads us to the withdrawing of some Egyptian seeds from the EU market and to a temporary ban on imports of all seeds and beans originating from that country," said EU Health Commissioner John Dalli.
Egypt's ministry of agriculture last week denied fenugreek seeds exported to Europe had caused an E.coli outbreak that has killed 50 people, mainly in Germany.
The head of Egypt's Central Administration of Agricultural Quarantine, Ali Suleiman, said claims by EFSA that seeds exported in 2009 and 2010 may have been implicated in the outbreak were "completely untrue."
"The presence of this bacteria in Egypt has not been proven at all, and it has not been recorded," Suleiman told the official MENA news agency.
He said the Egyptian company that exported the seeds in 2009 has stressed in a letter that it had exported the fenugreek to Holland and not to Germany, Britain or France.
The World Health Organisation has said 4,050 infections have been confirmed in 14 European countries, the United States and Canada - more than 3,900 of them in Germany.
All but two of the fatalities have so far been in Germany, apart from one case in the United States and a woman who died in Sweden shortly after returning from a visit to Germany.
The outbreak in France claimed the life of a 78-year-old woman late last week.