India and Italy should work toward an agreement to allow an Italian marine to return home while an arbitration process continues in the fatally shootings of two Indian fishermen in 2012, a tribunal said Tuesday.

The two countries should present their arguments over relaxing the marine's bail conditions to India's Supreme Court, the tribunal in The Hague said.

The case against Salvatore Girone and another Italian marine, Massimiliano Latorre, has strained relations between the two countries, which disagree on the facts of the case and who has jurisdiction. Italy has also complained bitterly about the fact that, in four years, India has never formally charged the two with a crime.

An arbitration tribunal is hearing the dispute over jurisdiction, and in the ruling announced Tuesday said the two countries should approach India's Supreme Court about changing Girone's bail terms to allow him to return to Italy. Latorre has been in his home country since September 2014 on medical treatment after suffering a stroke in India.

Both India and Italy welcomed the tribunal's ruling, which had been shared with officials from the two countries on Monday. India was happy that the ruling confirmed its jurisdiction to decide bail, while Italy found relief in the possibility of Girone's return.

"We see the tribunal's order not just as a recognition of India's consistent positions and key arguments but also as an affirmation of the authority of the Supreme Court of India," Indian Finance Minister Arun Jaitley, speaking Tuesday in Parliament on behalf of the foreign affairs minister.

In Rome, the defense minister expressed confidence that Italy would be proven right through the arbitration process.