Sheikh Hasina said in an interview with the Sunday Express that her government had passed on concerns about a number of unidentified “incidents” to the authorities in Burma where there have been clashes between Buddhists and Muslims.
The recent fighting, which has seen dozens killed, has been taking place in the western Burmese state of Rakhine.
Thousands of Rohingyas, whom the UN describes as a persecuted Islamic minority group in Buddhist Burma, have tried to flee to Bangaldesh, a secular country of 160 million mainly Muslims.
Sheikh Hasina’s Awami League government has been turning them away at the border, angering campaign groups Human Rights Watch and Amnesty.
However, she told the Sunday Express that the international community should investigate why so many are fleeing.
She met Foreign Secretary William Hague earlier today to discuss the situation.
In her interview with the Sunday Express, she said she was concerned about the activities of Jamaat e Islami, an Islamic fundamentalist political party that has a powerbase near the border with Burma and which has previously been accused of terror links, allegations it denies.
She alleged: “Jamaat e Islami is very much involved in terrorist activity, there’s no doubt about it and everybody knows that.
“As for refugees, we have a large number trying to get into our country, which is already over-populated.
“How many can we take it? We don’t want any refugees coming to Bangladesh. “The international community should try and find out why these refugees want to come.”
Asked if she was concerned that Jamaat e Islami might be encouraging some refugees, she said: “We have some intelligence reports about it.
“My government has talked to our ambassador in Myanmar (Burma) and they have informed them about some incidents and our intelligence people and law enforcement agencies are enquiring about it.
“We are trying to find out the reality.”
Sheikh Hasina, who attended Friday night’s Olympic opening ceremony, also praised Britain and Scotland Yard for helping in the fight against terrorism.
She came to power in 2008 after several years of rule by the military and the Bangladesh Nationalist Party, whom
she accused of being soft on terror.
She said: “Our position is a zero-tolerance to terrorism. Many people were killed between 2001 and 2006 but but since we formed our government we will not allow anybody to use our soil to launch any type of terrorist activity.”
“But once a previous government encouraged them or nursed them, you cannot stop them overnight.
“We have good relations especially with the British. We have a Joint Task Force on Counter Terrorism and they are training our people and that is really very helpful and I really appreciate that.”
She also thanked UK taxpayers for the £250million of foreign aid sent from Britain every year, cash she says is
helping her vision to make Bangladesh a “middle income country” by 2021.
She already has a large-scale infrastructure improvement programme in the country and is also working with neighbouring Nepal, India and Bhutan about a massive tourism drive in the region.
She said: “We have the world’s longest naturally sandy beach (at Cox’s Bazar).
“We want to develop that with lots of beautiful tea gardens areas, so there is a very good possibility to develop this.”
In her meeting with Mr Hague today, the Rohingyas crisis was raised alongside other issues, including trade, migration co-operation and climate change.
Mr Hague said: “The strong roots between our two countries are reflected in our trade relationship where the UK is the largest cumulative investor in Bangladesh.
“I welcome our co-operation on a range of international issues not least climate change, where Bangladesh plays an important role.”