"There is little to be gained by appearing before such a fundamentally flawed commission," said HRW's Executive Director Kenneth Roth in a statement.
"Accountability for war crimes in Sri Lanka demands an independent international investigation."
The rights groups have long accused government forces of ordering civilians into a "no-fire zone" and shelling them in the final stages of fighting between government troops and Tamil Tiger separatist rebels in early 2009.
The three groups have said that up to 30,000 ethnic Tamil civilians perished in the final months of the conflict, which ended when the rebels were wiped out in May.
In a joint letter to the LLRC, they said it would be impossible to have a free and independent inquiry in Sri Lanka even more