The party also demanded that both Singh and Gandhi should assure the country on the safety of women.
"The Prime Minister ought to have spoken to them. The police ought to have been sensitive. The way they have been lathi charged, water cannon thrown at them and also the whole handling of the police and the administration is deeply regrettable and condemnable. BJP condemns the police action outright," party Chief Spokesperson Ravi Shankar Prasad said.
He asked both the Prime Minister and UPA Chairperson to break their silence, saying, "Why is the Prime minister silent. The whole nation is angry and Prime Minister has not said anything.
Prime Minister should speak up."
"We would like to appeal to you. Please don't maintain silence today. Delhi wants assurance. Young boys and girls want assurance. People of the country want assurance that they will be given security and safety."
He said women, children, young girls and even elderly are feeling insecure, and the protesting youth need to be handled by the authorities with sensitivity as they are deeply hurt and
"The police should respond in a sensitive manner to the deep sense of pain, agony and concern of the people of the country and the young people today," he said.
Several rounds of teargas shells and water cannons were used as protesters demanding justice for the 23-year-old gang-rape victim clashed with police at the Raisina Hill, the seat of power.
Resort to firing of shells and water jets failed to dampen the spirit of several hundreds of young students, both girls and boys, as they tried to breach the police barricades to march towards Rashtrapati Bhavan for the second day protesting against government and police "inaction" in the gang-rape case.
Prasad also asked the government to help the victim get the best medical treatment and if need be sent abroad for procedures not available here.
"The girl has to live and government should ensure that she gets the best treatment and if need be even from abroad," he said.