Lawmakers said Singh told them he would ask his external affairs minister to take up the issue with the Italian government, the Press Trust of India reported.
Marines Massimiliano Latorre and Salvatore Girone face charges in the 2012 deaths of two fishermen they mistook for pirates off the Kerala coast.
They returned to Italy to vote in last month's special election after receiving special permission from India's Supreme Court.
The Italian Foreign Ministry said India has not responded to its requests to seek a diplomatic solution and a formal dispute now exists between the two countries under the United Nations' Law of the Sea Convention.
Notable deaths of 2014 [PHOTOS]