The Burma Government says about 400 people have been killed in the fighting.
Hasina, who will address the annual gathering of world leaders at the United Nations General Assembly later this week, said Trump's stance on refugees is clear, so it's not worth asking him for help with the Rohingya Muslim refugees.
"Already America declared that they will not allow any refugees," she said.
"What I can expect from them, and especially (the) President. He already declared his mind ... so why I should ask?"
Hasina added: "Bangladesh is not a rich country ... but if we can feed 160 million people, another 500 or 700,000 people, we can do it."
A senior White House official was unaware of the exchange but said Trump was deeply interested in the subject and that "he would definitely engage if it were brought up".
Shortly after taking office in January, Trump tried to put a 120-day halt on the US refugee programme, bar Syrian refugees indefinitely and impose a 90-day suspension on people from six predominantly Muslim countries.
- Reuters, AAP