Jayalalithaa in line with her strict anti-Lanka stand had on Sunday ordered sending back two different teams of Sri Lankan footballers.
One team had flown down to Chennai and played a friendly with customs department. A Lankan school level football team was also asked to leave.
"All that we can insist is there should be no military training to Sri Lankan personnel in India as the military was responsible for death of civilian Tamils (during the armed conflict). That is what we have been striving for and even stoutly opposing in Parliament," Karunanidhi told reporters.
The DMK chief, whose party is a key UPA ally, was replying to a query on Lankan pilgrims being forced to leave for home after some local pro-Tamil outfits staged a protest against them near Thanjavur yesterday.
He said it is usual for sportsmen, especially cricketers from both nations to travel to either country to play matches as the Indian cricket team is all set to travel to the island nation for the ensuing T20 World Cup.
On Lankan President Mahinda Rajapakse's proposed India visit later this month on an official engagement, Karunanidhi said, "It is not acceptable to us that he who is responsible for the killing of lakhs of Tamils is accorded a special welcome" in India.
On the issue of 'coalgate', he rued stalling of Parliament (by the BJP).
"Where else shall the matters be debated if Parliament is stalled," he said.