Payao Akkahad, mother of a paramedic who was shot and killed during political disturbances in 2010, is the bill's major backer, the Bangkok Post reported Saturday.
She said it has no color, referring to the red, yellow and other shirts worn by members of various parties during demonstrations.
"We are not concentrating on Pheu Thai and the Democrats as they are the conflicting parties," she told radio station FM 100.5.
Payao wants quick action on the bill, which would cover the period from the coup that ousted Prime Minister Thaksin Shinawatra to May 9, 2011, when the campaign that led to his sister, Yingluck Shinawatra, becoming prime minister began.
The new amnesty proposal was drawn up by people like Payao who lost relatives during the period of unrest. It would not protect those who committed violent acts.
Parliament reconvenes in August.
Notable deaths of 2014 [PHOTOS]