Singh conveyed this to delegations of Kerala MPs from Left and Congress, who met him separately to express anguish and demand his intervention in the "serious" matter.
The Prime Minister said it was "unacceptable", according to CPI(M) MPs K N Balagopal and M B Rajesh.
Singh told the Left MPs that he will ask External Affairs Minister Salman Khurshid to take up the issue with Italy.
The two marines are facing trial for allegedly killing two fishermen off the Kerala coast in February last year, mistaking them for pirates.
The Italian Ministry claimed India had not responded to its requests to seek a diplomatic solution to the case and there was now a formal dispute between the two countries over the terms of the United Nations Convention of the Law of the Sea.
"We will study and take a rightful position... We will take informed position," he told reporters on the issue which is very sensitive in Kerala politics.
Rajesh said, "We met the Prime Minister and took up the issue of Italian marines. The Prime Minister told us that he came to know about this from newspapers. He assured us that he will ask the External Affairs Minister to look into this issue to intervene in this issue.
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