Hasina spoke about the matter at a meeting of the ruling Awami League after visiting Turkish First Lady Emine Erdogan met her at the Ganabhaban on Thursday.
"People are fleeing to Bangladesh for shelter after losing everything in one incident after another. We are trying our best to help them," she said.
"In addition, we are pressuring the Myanmar government so that they take back their people from our country. That's what we want," she added.
Bangladesh has sheltered hundreds of thousands of Myanmar Rohingyas, including around 164,000 in recent weeks, according to UN estimation.
Myanmar does not recognise Rohingya people as its citizens neither has it responded to Bangladesh's frequent calls to take back the refugees.
A crackdown by the Myanmar Army on Rohingya insurgents after killings of 13 members of the security forces in Rakhine State on Aug 25 has left nearly 400 killed, including civilians, the Myanmar authorities said.
Hasina said Myanmar is bringing 'dishonour' to itself by forcing its people to become refugees in another country. "Myanmar has to understand this," she said.
"Myanmar should take back those who have come to our country for shelter, and ensure their security and means of livelihood."
"Incidents in Myanmar have been pushing refugees into Bangladesh since 1974. There are more unregistered refugees than those registered," she added.
The prime minister said she was sad about the ‘insufferable’ misery of the Rohingya women and children.
"The most inhumane side of this situation is that the women and children are in misery; newborns are dying. Only hearing about something like this causes pain. It is unbearable," she said.
Turkish President Recep Tayyip Erdogan's wife Emine has visited Bangladesh to meet the Rohingya Muslims who have escaped atrocities in Rakhine.
Facing widespread criticism over the persecution of the Rohingya people, Myanmar leader Aung San Suu Kyi said earlier in the day that her government was doing its best to protect everyone in Rakhine.
She, however, did not refer specifically to the exodus of the Rohingya despite Western critics accusing her of not speaking out for the minority group.
Many in Buddhist-majority Myanmar see the Rohingya Muslims as illegal migrants from Bangladesh.