Rallies, candle-light marches were organised demanding that the culprits be hanged.
A 22-year-old man was arrested for allegedly making vulgar comments on the social media about the veterinarian.
He was arrested after cyber crime police in Hyderabad registered a case on November 30 after some unknown people uploaded photos of the victim and made objectionable comments about her, a senior police official said.
A protesting woman lawyer claimed that existing laws, which were made during the British raj, needs to be changed.
Congress activists led by head of women's wing Nerella Sarada held a protest at Patancheru, demanding prohibition on liquor and control of obscene videos and films.
Consumption of alcohol and watching obscene videos are contributing to a rise in crimes against women, she claimed.
A fast track court should be set up to try the case and the culprits punished within a month, Sarada said.
Candle light marches were organised in Hyderabad and elsewhere against the incident.
State Finance Minister T Harish Rao said parents should check the behaviour of their sons and help in moulding them as responsible citizens.
Education Minister P Sabitha Indra Reddy, speaking at an event here, said teachers should guide the students in imbibing discipline.
Meanwhile, the petition filed by police in a court at Shadnagar here, seeking custody of the four accused in the case, is likely to come up for hearing on Wednesday.
Taking a serious view of some news channels and social media sites disclosing the identity of the 25-year-old woman veterinarian, besides airing images of the accused, the police on Tuesday issued notices to them with a direction to stop it.
The police had said the victim's real name should not be used in media and social media and requested them to refer to her as "#Justice for Disha" to protect anonymity, confidentiality and the rights of the victim's family.
The gruesome rape and murder has led to a nation-wide public outrage.
The charred body of the woman, working as an assistant veterinarian at a state-run hospital, was found under a culvert in Shadnagar near here on November 28 morning a day after she went missing.
The four men, all lorry workers, aged between 20 and 24, were arrested on November 29 for allegedly raping and killing the woman by smothering her and later burning her body.
The four are under judicial custody and lodged in high security cells in Cherlapally Central Prison here where police tightened security by deploying additional personnel.