"If rumours are spread, strict action will be taken against those who indulge in such activities," he told reporters outside Parliament House.
He said the Prime Minister and he himself have spoken to the Karnataka chief minister, requesting him to ask the people to share information on rumour mongers.
Asserting that the situation in the state was peaceful, he said extra trains have been pressed into service for Assam to help people who want to leave Karnataka.
Shinde said 300 people left last night and two extra trains are pressed into service today for Assam.
Over 5,000 panic-stricken people from North Eastern states fled Bangalore yesterday after rumours of attacks targeting the community spread.
Karnataka Chief Minister Jagadish Shettar is holding a high-level meeting to tackle the situation.