"His vehicle was precisely targeted, because there were several vehicles travelling along this road. It's another example of how the regime in Colombo acts."
The military has denied any responsibility for the politician's death.
"We don't know what exactly happened because it has occurred in an uncontrolled area," Brigadier Udaya Nanayakkara, a military spokesman, said.
"There are no deep penetration units operating in that area. We totally deny it."
Sivanesan had attended a meeting in parliament the previous day.
"He left the parliament quarters after attending the parliament sessions yesterday," Suresh Premachandran, a fellow TNA legislator, said.
"Most probably in those areas the army is deploying deep penetration units. This fellow is a victim of that."
Three of the TNA's 22 MPs have been killed since fighting between the government and the rebels resumed in 2005.
Joseph Pararajasingham, a representative for the eastern Batticaloa district, was shot and killed at a 2005 Christmas mass.
His colleague, Nadarajah Raviraj, was killed in the capital, Colombo, in November 2006.
The TNA blamed those two killings on government-backed paramilitary groups, a charge the authorities denied.
An estimated 70,000 people have died in the conflict since 1983.