However, heavy gunfire resumed on Thursday at the border guards' barracks in the Pilkhana area of Dhaka, where a small number of guards had begun surrendering their weapons.
Schools in the surrounding area have been closed for the day.
Mobile phone services have been suspended across the country, the Bangladesh Telecommunication Regulatory Commission said, in a bid to stop the rebellion spreading, although there is thought to be service in some parts of Dhaka.
The BDR has 70,000 men stationed at 42 camps across the country, including 40,000 on the borders.
There have been reports of rank-and-file soldiers seizing control of their barracks and camps in at least 12 different towns and cities since early on Thursday.
In some cases, the border guards have taken their officers hostage, and in others they have forced them to leave, reports say.
There are unconfirmed reports of gunfire in the main port city of Chittagong, at Feni, on the eastern border with India, in Rajshahi in the north west, and Sylhet in the north.
A man claiming to be a BDR soldier in Chittagong said they had opened fire to prevent regular army units from entering their camp, unconfirmed reports say.
Another report said similar incidents had occurred at Cox's Bazaar and Feni.
In Khulna in the south, border guards have reportedly blocked a road, but no shooting has taken place.
BDR troops have released hostages taken on Wednesday
The police chief in the north-eastern Moulivibazar district told the AFP news agency that the border guards were "firing indiscriminately".
"Their commanding officer told me that he has fled the camp."
Indian border officials have told the BBC that all the posts on the West Bengal border have been closed, as have posts in the north-eastern state of Tripura.
Indian officials also say BDR troops have left their posts in the Lalmonirhat area in North Bengal.
There are no reports so far of any casualties in these reported incidents.
Some mutineers told the BBC that they took up arms over fears that regular army units had been ordered to disarm them.
Speaking on Wednesday, one told the BBC that the guards had had to take up arms to resolve problems with their officers.
"Our families might suffer because of what we have done, but they have been exploiting us for more than 200 years," the man said.
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