As the bloc's standing committee on food chain and animal health failed to reach a majority either for or against, the decisions will pass to an appeal committee over the coming weeks, a Commission spokesman said.
Should the appeal committee also be unable to reach an agreement, the Commission will be free to grant EU marketing approval.
Two of the applications are for maize varieties containing multiple or "stacked" gene traits. These are designed to protect the growing plants from multiple insect pests and both products are developed jointly by Monsanto Co and Dow Chemical Co.
Neither variety is approved for cultivation in Europe. The authorisation would cover the use of imports in food and feed products sold in Europe, although there is little or no demand for genetically modified food among EU consumers.
The third approval covers the pollen of Monsanto's insect-resistant MON810 maize. This is the only genetically modified crop which is currently grown commercially in Europe.
The bid for approval followed a ruling by the Europe's highest court in 2011 that even small traces of the pollen in honey must receive EU authorisation before the product can be sold.
Five out of 27 EU member states grew MON810 maize on 129,000 hectares in 2012, according to data from the International Service for the Acquisition of Agri-biotech Applications (ISAAA). Spain was the top producer, followed by Portugal, the Czech Republic, Slovakia and Romania.