He said he was disappointed at what took place at Low Yat Plaza and the comments on social media following Sunday's incident.
"The rakyat should not create racial hatred via the internet or messaging apps on their phones.
"I have ordered the Home Ministry and Malaysian Communications and Multimedia Commission to monitor them thoroughly and at the same time I will use the relevant Acts, especially the Sedition Act, against those who destroy racial harmony," said Najib in a Mandarin statement on his Facebook page.
"About the Low Yat incident in Kuala Lumpur which escalated into a violent brawl, which later transformed into a heated racial topic online.
"I am disappointed at this phenomenon. The police have taken action against those involved in the crimes and also the troublemakers. Everyone must stop spreading rumours and rely on official statements issued by the police," said Najib.
On Sunday, five people, including two journalists, were injured in a mob attack at the plaza in Bukit Bintang which was sparked by what police said was due to a shoplifting incident earlier in the evening.
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