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Reflecting growing anger in India, the normally mild-mannered Singh told MPs it was "unacceptable" that both men had remained in Italy after being allowed home to vote in elections last month.
"This cannot by any standards be in the interests of any bilateral relationship that has to function on the basis of trust," said the premier, whose government is under intense pressure to take action against Italy.
"Our government has therefore insisted that the Italian authorities respect the undertakings they have given to the honourable supreme court and return the two accused persons to stand trial in India.
"If they do not keep their word, there will be consequences for our relations with Italy."
Singh's comments come after Italy's ambassador, Daniele Mancini, was summoned to the foreign ministry on Tuesday where India's Foreign Secretary Ranjan Mathai demanded Rome immediately hand over the marines.
Reports in newspapers including the Times of India and the Indian Express have said that Mancini could now be expelled after he gave his personal assurance in the Supreme Court that the two men would return.
Massimiliano Latorre and Salvatore Girone are accused of shooting dead two fishermen off India's southwestern coast in February last year, when their fishing boat sailed close to the Italian oil tanker they were guarding.
The marines said they mistook the fishermen near the port of Kochi in Kerala for pirates. They were granted leave by India's top court to return home for four weeks in order to vote in the February 24-25 polls.
But the Italian foreign ministry announced Monday that the pair would not return to India once their leave expires in view of a "formal international controversy" between the two countries.
Italy insists the marines should be prosecuted in their home country because the shootings involved an Italian-flagged vessel in international waters, but India says the killings took place in waters under its jurisdiction.
The case was initially heard in a local court in Kerala but it was later transferred to the Supreme Court in New Delhi which ordered that a special court be set up for the trial.
Relations between the two countries have also been soured by corruption allegations surrounding a $748 million deal for the purchase of 12 Italian helicopters which the Indian government is now threatening to scrap.
In the wake of the announcement that the marines would remain at home, Singh's rivals in the main opposition Bharatiya Janata Party (BJP) accused Italy of treating India like a "banana republic".
In a sign of the anger over the government's handling of the crisis, effigies of Singh were burned Wednesday in Kerala's capital Thiruvananthapuram.
Speaking in Delhi, Mancini said he was "confident that the two mature democracies such as ours will overcome these difficulties".
"We are working with Indian institutions and government to do whatever best can be done to overcome these current difficult moments," he added.
However Kerala Chief Minister Oommen Chandy said there could be no compromise on the issue and the marines had to face trial in India.
"How can a country use its diplomatic status to cheat the apex court of another nation? If Italy fails to fulfil its word, it will be a diplomatic tragedy," Chandy was quoted as saying by the Press Trust of India.
Even the marines' Indian lawyer has washed his hands of the pair.
"I consider this action of the Republic of Italy as a breach of faith," Harish Salve said in a statement Wednesday.
"In these circumstances, I have informed the Italian ambassador that it will no longer be possible for me to appear, for me to be associated with this case."