The calls follow a report by Europe's food safety watchdog this week dismissing the study's findings.
Reed Elsevier, which published the study in its Food and Chemical Toxicology journal in September, said on Friday it was considering the criticisms and would let readers know if it concluded it needed to change the way it checked research.
In a statement on its website, the journal said "the paper was published after being objectively and anonymously peer reviewed, with a series of revisions made by the authors and the corrected paper then accepted by the editor."
Hundreds of scientists from around the world have questioned the research, which was written by French researcher Gilles-Eric Seralini of the University of Caen and said rats fed on Monsanto's GM corn suffered tumors and multiple organ failure.
Genetically modified crops are deeply unpopular in Europe but are common in the United State where they have been grown and consumed for more than 15 years.
A day after the study was published, Seralini defended his work, saying it was the most detailed study on the subject to date.
But more than 700 scientists have signed an online petition calling on Seralini to release all the data from his research.
The petition, addressed directly to Seralini, says: "Only a full disclosure of the data can quell any uncertainties over the results you published."
The chief executive of the agricultural research centre Rothamsted Research, Maurice Moloney, said Seralini's study was "seriously deficient in its design, its execution and its conclusions" - failings compounded by "excessive secrecy around the data".
In a letter to the journal's managing editor Bryan Delaney, Moloney said it was "appalling that such work should appear in a respected Elsevier journal".
He also demanded to know how the paper managed to pass peer review - a process in which other scientific experts check a study, analyze its methods, question the authors and decide whether it is robust enough to give a reliable result.
Marc Van Montagu, president of the European Federation of Biotechnology, said this was "a dangerous case of failure of the peer-review system, which threatens the credibility not just of the journal but of the scientific method overall."
Cathie Martin, a scientist at the John Innes Centre for plant science and microbiology research, said in the light of such widespread criticism of Seralini's study, "is it not time for Food and Chemical Toxicology to retract the manuscript?"
The European Food Safety Authority (EFSA) issued a statement earlier this week confirming the findings of its initial review saying Seralini's study had "serious defects" in design and methodology and "does not meet acceptable scientific standards".
Among other criticisms, the EFSA review panel said the authors had failed to establish appropriate control groups as part of the study, and had chosen a strain of rat that is prone to developing tumors during its normal lifespan.
Six separate national food safety bodies also asked to review the study - in France, Germany, Denmark, the Netherlands, Italy and Belgium - also came to the same conclusions.
(Reporting by Kate Kelland, editing by Andrew Heavens)
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