In an interview on Monday, the Karen leader had predicted a possible increase in violence ahead of a constitutional referendum in Myanmar in May.
His son Hse Hse, another senior member of the predominantly Christian Karen rebel movement, blamed a Buddhist Karen splinter group which brokered a truce with the Myanmar government in the mid-1990s.
"This is the work of the DKBA and the Burmese soldiers," Hse Hse said, referring to the Democratic Karen Buddhist Army.
The KNU and its armed wing, the Karen National Liberation Army (KNLA), are riven by internal feuds and lethal vendettas.
Thai police said they had the registration number of the vehicle and were setting up roadblocks around Mae Sot - a frontier town of refugees, illegal migrants and gem dealers - to try to catch the two killers.
The Karen have been fighting for independence in the hills of eastern Myanmar for the past 60 years.
The group once controlled areas of eastern Myanmar, but has been reduced mainly to a string of bases pressed against the Thai border.
Myanmar began a bloody offensive against the Karen two years ago, which activists say has targeted ordinary villagers rather than separatists.
Decades of fighting have devastated eastern Myanmar, where 500,000 people have been displaced by violence, according to Human Rights Watch, a New York-based rights group.
Up to 150,000 Karen refugees also live in camps along Thailand's border with Myanmar. Many of them have been there for more than 20 years.
Rape, forced labour, summary executions and land grabs remain widespread, while the military also forces villagers to act as human minesweepers, Human Rights Watch said in its annual report last month.