Police sources quoted by news agency IANS said that the alert had been issued to several states and union territories which have Jewish synagogues, sizeable Jewish residents or attract Israeli tourists.
"We have to keep a look out and secure areas frequented by Israeli tourists as well as a prayer house they have in North Goa. The threat, according to the inputs, comes from a possible attack by Islamic State or the Al-Qaeda to avenge for the New Zealand mosque killings," a senior police official said on condition of anonymity.
Goa is a preferred destination for hundreds of Israelis who are generally on long-duration visas and often congregate to pray at a Chabad house (a Jewish outreach centre) in North Goa.
Meanwhile, the body of a 27-year-old woman from Kerala, who was among the 50 killed in Christchurch terror shootings, was brought to the state Monday and laid to rest.
Prayers were held at the Cheraman Juma mosque at Kodungallor before the body of the woman, Ancia Alibava, was laid to rest. The mosque is said to be the oldest in the Indian subcontinent.
Ancia was pursuing her M.Tech degree in an agricultural university in New Zealand.
She had gone to the mosque to offer prayers along with her husband Abdul Nazar when the shooting took place on March 15 during Friday prayers, reported news agency PTI.