The 16-member delegation led by the Senate's Chairman of the Committees on External Affairs Pier Ferdinando Casini held talks with European Union ambassador and number of EU diplomats seeking their support on the issue.
Home Ministry has already given sanction to NIA to prosecute the marines under Suppression of Unlawful Acts Against Safety of Maritime Navigation and Fixed Platforms on Continental Shelf Act (SUA). The SUA provides for death penalty.
Italian marines Massimiliano Latorre and Salvatore Girone, who were on board Italian vessel 'Enrica Lexie' and now lodged in Italian Embassy premises here, allegedly shot dead the two fishermen off the Kerala coast on February 15, 2012.
In the meetings, the delegation, which arrived here yesterday on a two-day visit, underlined the "international repercussions" of the issue and sought its amicable resolution.
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The delegation said it wanted to initiate dialogue at parliamentary level aimed at facilitating an appropriate and honourable solution to the issue, in the light of the traditional friendly ties that the two nations have always maintained.
The Supreme Court had shifted the case to Delhi, saying the Kerala Police had no jurisdiction over it and backed the government's decision to hand over the case to NIA.
The Italian government has already challenged before the Supreme Court invoking of anti-terrorism law SUA, saying it is against the order of the apex court which allowed proceedings only under the Maritime Zone Act, IPC, CrPC and UNCLOS.