The four marines were issued the summons to be witnesses by India's National Investigation Agency (NIA), the semi-official Press Trust of India reported.
The marines were aboard the Italian vessel "Enrica Lexie" when their colleagues, Massimiliano Latorre and Salvatore Girone, allegedly shot dead the two fishermen in February last year off the southern Indian coast of Kerala.
The four marines said they were not ready to come to India to be witnesses in response to the summons from the NIA, which is probing the case, official Indian sources were quoted as saying by the Press Trust of India.
The witnesses said they were willing to appear through video conferencing, or an NIA team could visit Italy to question them or the Indian investigators could send them written questions to which they would reply.
However, the Indian sources said none of the proposals was acceptable to the NIA investigators.
Faced with the four witnesses' refusal to come to India, the Home Ministry has sought opinion of the Law Ministry on the future course of action, the sources said.
The news agency said the refusal of the Italian witnesses to come to India would delay the trial of the two Italian marines, who have been at the Italian embassy in New Delhi awaiting hearing of the case.
India in April told Italy preparations to set up a special court to try the marines who are facing murder charges over the deaths were at "an advanced stage", the Press Trust of India had said.
Italy's government has been worried that the trial of the two men would get bogged down in India's slow legal system.
The two marines returned for trial in March after Rome initially refused to send them, triggering a bitter diplomatic stand-off between India and Italy.
The marines were guarding an Italian oil tanker when they opened fire on a fishing boat and the two fishermen were killed.
The marines say they mistook the fishing boat for a pirate vessel.
Italy had insisted the pair should be prosecuted in their home country because it said the shootings involved an Italian-flagged vessel in international waters.
India says the killings took place in waters under its jurisdiction.
India, which uses the death penalty in what it says are the "rarest of rare cases", has assured Italy that the two men will not face execution.
The return of the two marines caused huge controversy in Rome and prompted Italy's foreign minister to resign in protest.