The commission took note of the decision of the Italian authorities to send back to India the two marines, Massimilian Latorre and Salvatore Girone, but "we have no details of the arrangement", a spokesman said.
The commission hopes that the "dispute over the substance of the issue will be resolved soon," he told reporters.
Asked whether the Italian government had informed the commission about its intention to change its position, the spokesman said the commission has been in close contact with the Italian authorities since the row between the two nations broke out, but on this specific question he has no information.
Three days ago, the row between India and Italy appeared to drag the European Union into it after EU foreign policy chief Catherine Ashton warned India that it would be violating international law on diplomatic immunity by preventing Italian ambassador Daniele Mancine from leaving the country.
Ashton had expressed concern over Indian Supreme Court order on Monday, barring the Italian ambassador from leaving the country without its permission until further orders.
She had warned India that any limitations to the freedom of movement of ambassador Mancine would be in violation of the 1961 Vienna Convention on diplomatic relations.
The Indo-Italian diplomatic row was sparked off by the Rome government's announcement last week that it will not send the two marines back to India to stand trial in the murder of two Indian fishermen.
Italy also questioned India's jurisdiction in the case as it claimed that the shooting of the two fishermen by the marines, who were part of an armed patrol guarding an Italian oil tanker, took place in international waters.
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