The premier, however, added that vacant posts under quotas will be filled with candidates from the merit list.
Prime Minister Sheikh Hasina said on Thursday that it is not possible to remove the quota for freedom fighters in government jobs, as there is a High Court verdict requiring it to be continued.
"There is a High Court verdict ordering the maintaining of the freedom fighter’s quota. How can we violate a High Court verdict? We can't do this," she said during her valedictory speech at the 21st (budget) session of the current parliament.
The leader of the House said: "I said earlier that we [the government] will terminate the entire quota system, but now there is a High Court verdict in this regard. If I violate the verdict, I'll face contempt of court. No one can do this."
Sheikh Hasina did however add that vacant posts set aside for quotas will be filled with candidates from the merit list.
"This process has been continuing for the last several years."She also said, "I formed a committee headed by the Cabinet secretary which is now looking into the matter. Then where's their (demonstrators) problem?"
Pointing to the quota reform movement, Sheikh Hasina said the demonstrators also cannot say what they actually want.
Coming down heavily on those who attacked the Dhaka University Vice-Chancellor's residence, she said anyone who vandalised, attacked, or set fire to cars and looted valuables at the VC's residence will not be spared.
"They can't be spared. So, they're being arrested and an investigation is underway. Many of them have already confessed," she said.
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The prime minister said there is no country in the world to get higher education at such a low cost than what is available in Bangladesh. Students are staging demonstrations paying only Tk15 a month in rent for the dormitory housing they live in and pay only Tk30 for a meal.
"Is it a movement? It's a chaos, which will never be tolerated" she said, pointing to the vandalizing of a dormitory gate and female students coming out of their dormitories at midnight.
"If so, let them pay the seat rent and meal charge at market prices," Hasina said.
The premier praised the Opposition Leader and all the MPs for playing a very constructive role in the budget session.
She said a decent and fair atmosphere prevails in the current parliament.
"Parliament is run the way it should, in a democratic way" she added, echoing the views of Opposition Leader Raushan Ershad.
Hasina said this parliament formed by the 2014 elections did not see any unwarranted activity. "There were very constructive discussions enhancing the dignity of Parliament, to a large extent, before the nation."
About the next general election, the prime minister in a more than 50 minute-speech said she hoped that all, including the Opposition Jatiya Party, will participate in the polls.
"If people want, they'll give us the opportunity again to serve them y casting their votes in favor of the boat (the election symbol of Awami League)," she said.
Focusing on various development activities of the government, Hasina said Bangladesh is marching forward and will do so."Nobody can stop Bangladesh now.