Activists have given the police investigation into the attack on Sirawith Seritiwat one week to make significant progress.
"If there is no progress in seven days, anything that happens afterwards may get out of control," said Adul Khiewboriboon, chairman of the support group for relatives of victims of the 1992 Black May unrest.
"I am not making a threat but it is impossible that security agencies do not know (who attacked him)," he added.
Sirawith, known as "Ja New", was savagely beaten by four men near his house in Klong Sam Wa district on Friday. He is still in serious condition at Ramathibodi Hospital.
His mother, Pattanaree Charnkit, said Mr Sirawith's condition had improved slightly, but he is still being carefully monitored by doctors who need to perform surgery on his nose.
"I feel a bit relieved as he is in the capable hands of doctors. He has regained consciousness since the attack, but his responses are very slow," she said.
"'New' has not lost his eyesight, but his vision is not clear," she added.
The assault on Mr Sirawith was the second in one month and so far police have found no suspects in either crime. The activist was attacked in Huay Kwang district on June 2.
Police held an urgent meeting on Sunday after national police chief Chakthip Chaijinda was ordered to find the attackers.
Pol Gen Chakthip said on Sunday that progress is being made in the probe but refused to go into details. The police chief did not elaborate on the evidence of security footage that appeared to show two of the four men who assaulted him on Friday.
Ms Pattanaree said investigators have contacted her son for information, but he refused to talk to the police until his condition improves.
Mr Sirawith is a staunch critic of the military coup and regime.
