They were detained on Sunday from the Italian ship Enrica Lexie and produced at the magistrate's court on Monday.
The incident took place off the coast of the southern state of Kerala last Wednesday.
Italian officials said the Indian fishing boat had behaved aggressively and ignored warning shots.
They said they opened fire, mistaking the fishermen for pirates. India said the fishermen were unarmed.
The incident has sparked a major diplomatic row between the two countries, with Indian police opening a murder inquiry into the deaths.
Indian Defence Minister AK Antony has described the killings as "very serious" and an "unfortunate incident".
The Italian ambassador in Delhi was summoned by the foreign ministry on Thursday over the shooting.
More questioning
On Monday evening, the magistrate in Kerala's Karunagappally town sent the Italian marines - identified as Latorre Massimiliano and Salvatore Girone - into judicial custody for 14 days.
For the first three days of their custody, the marines have been handed over to the police and taken to the port city of Kochi for questioning.
The Italians were produced at the magistrate's home amid protests by local people close to the dead fishermen who demanded that the Italian vessel's captain be arrested.
A delegation of experts from Italy's foreign, defence and justice ministries arrived in Delhi on Sunday to discuss the case with Indian officials, but the two sides have so far been unable to resolve their differences.
Italy insists that its personnel cannot be charged under Indian law. It says the marines have immunity as the tanker was flying an Italian flag and was in international waters when the incident happened.
But India wants the marines to be tried under local laws and has registered a case of murder against the men who could face the death penalty or life imprisonment if they are found guilty.
The Enrica Lexie was on its way from Singapore to Egypt, with a crew of 34, including 19 Indians. The Italians say the crew members fired in self-defence - after initially firing warning shots - because they feared their vessel was about to be attacked.
Indian officials say they are surprised at the shooting, maintaining that the fishermen did nothing to threaten the Italian ship.
A senior official in Kerala, PG Thomas, said the attack was unwarranted as there were "no weapons on the trawler".
Indian officials said nine of the 11 fishermen in the trawler were asleep and the two victims were steering it when the incident happened.
Following the incident, the Indian coastguard sent two boats and an aircraft to intercept the ship which is now anchored off the port of Kochi.
The Kerala state government has authorised a payment of 500,000 rupees ($10,125; £6,450) each to the dead fishermen's families.
Piracy has emerged as a major threat to merchant ships in the Indian Ocean and the Arabian Sea, with Somali pirates hijacking ships and their crews for ransom.
But there have been fewer attacks recently, partly because more armed guards are now deployed on board ships.