After President Yoon Suk Yeol blocked a bill to launch a new probe into the deadly incident.
It killed 159 people in Seoul's Itaewon district on Halloween.
Yoon's office announced the decision hours after the prime minister branded the opposition-backed bill as politicized and potentially in breach of the constitution.
The move to block the bill has been heavily criticized by relatives of the victims and opposition party officials.
They have long argued the government's handling of the disaster had been inadequate.
Shin Jung-Seob, the father of one of the victims, condemned the move.
"The government decided to cover up the incident without probing the truth. This stamps on the victims' last wishes to become a cornerstone to make the Republic of Korea more safe."
Lee Jeong-Min, the father of another victim.
"How can the government ignore the responsibility of finding out the truth and insult the victims and their family members by using money? I'm beyond feeling miserable, I feel indescribable anger."
Last year, a police investigation concluded that a lack of preparation and an inadequate response were the main cause of the deadly crush.
And prosecutors charged the head of the Seoul Metropolitan Police Agency earlier this month with contributing through negligence to the disaster.
But the United Nations Human Rights Committee said last year that South Korea should establish an independent and impartial body to investigate the disaster and ensure those responsible are brought to justice - including top officials.
No senior government figures have resigned or been sacked over the crush.
The leader of South Korea's main opposition party called the Yoon administration "cold-blooded" for blocking the bill.
The special bill put forward by parliament planned to include a panel appointed by the ruling party, the opposition and relevant groups to lead a fact-finding investigation.
It was supported by opposition parties but criticized by the ruling People Power Party (PPP), which said the panel would be biased in favor of the opposition.
