Both parties have traded blame for the violence, which has triggered an unprecedented communications blackout that shut down the internet and restricted phone services.
Before the Malaysians landed, Mr Mahmudin Abas, 70, said he last heard from his 26-year-old daughter Noorfaizzah on Friday before the internet was cut in Bangladesh.
Ms Noorfaizzah, a final-year medical student at Mymensingh Medical College, had planned to fly back to Malaysia on Thursday after the protests erupted, Mr Mahmudin said.
But on Thursday morning, she told her dad it became too dangerous to travel and was forced to return to her home near campus.
Mr Mahmudin said his daughter had not stocked up on enough food as she had not planned to stay, and she was then trapped indoors as clashes raged nearby.
“We started to panic. What if a building was burnt down and she had nowhere to go?” he said.
“She also told us that her friends who stayed in the student hostel had flown home a day earlier. But she’s staying alone near campus. So, there’s no guarantee of safety.”
On Friday, Mr Mahmudin and a group of parents of Malaysian students went to the Ministry of Foreign Affairs to ask for help and for authorities to take “quick action”.
“At that point they agreed to bring the students home as quickly as possible but they hadn’t decided to charter a flight,” he said.
Nevertheless, Mr Mahmudin was grateful to get confirmation from authorities that his daughter had managed to board the evacuation flight, expressing relief that she was physically fine.
Ms Fatihah’s father Dr Fadli Hamid, 53, said the parents started to take action after getting reports of rising food prices and student deaths due to the protests.
“When we heard that some students at Mymensingh Medical College had also died (in the protests), we decided that we could not do nothing and leave our children hanging,” he said.
When asked about accusations that the government did not act fast enough, Mr Saifuddin said the “bottom line” was that 123 Malaysians had arrived home safely.
“We sent a special flight there and they got back safely,” he said, adding that the evacuation operation was carried out “smoothly”.