"Earthquakes of this size have the potential to generate a widespread destructive tsunami that can affect coastlines across the entire Indian Ocean basin," the PTWC said.
"However it is not known whether a tsunami was generated."
Country authorities were asked to issue specific warnings if necessary.
The PTWC said if a tsunami was generated waves could reach Sri Lanka's coast at 4.09 pm hours (1039 GMT)at Trincomalee, at Dondra at 04.21 pm and Jaffna at 6.01 pm.
Residents in several parts of Sri Lanka reported feeling the quake.In December 2004 an tsunami from a much larger quake (9.6 on the Richter scale) devastated large parts of Sri Lanka.