Security has been increased at bus and train stations and airports.
Police in Mumbai are also searching for four men suspected of entering the city for the purpose of carrying out a terrorist attack. Computer-aided photographs of the four suspects were released.
India has taken even minor terror threats seriously since a three-day terrorist siege killed 166 people in Mumbai in 2008, though there has been no major attack there since.
In that attack two years ago, 10 armed terrorists fanned out across Mumbai attacking two luxury hotels, a Jewish center and a railway station.
In March, Mumbai police said they prevented a major terrorist strike after they arrested two Indian men, who, police said, were preparing to hit several targets in the city. Then in September, police issued a terror alert for the city during a popular Hindu festival.
The Associated Press contributed to this report.