The British-owned Asia Energy wants to develop an open-pit mine at Phulbari in Dinajpur district, 350km northwest of Dhaka.
Residents and rights groups say the mine would displace hundreds of families and damage the environment.
Asia Energy officials said on Monday they had withdrawn staff from Phulbari and cut operations in the mining area to a minimum.
The six demonstrators died on Saturday when police opened fire on a crowd near the Asia Energy office.
Police returned the bodies of the six to their families and Dinajpur district officials pledged to pay compensation to the relatives.
Tofayel Ahmed, a leader of the opposition party Awami League, said on Monday: "The casualties at Phulbari adds another black chapter to the country's history. We strongly condemn it and have called for the August 30 countrywide strike to voice our further protest."
Police say at least 120 people have been injured in clashes at Phulbari over the past two days.
The protesters have already enforced an indefinite strike from Sunday around the mining area and in nearby towns, local officials said.
On Monday, hundreds of protesters in Phulbari defied police warnings against demonstrations, blocking a train line and burning an effigy of Mahmudur Rahman, the government's energy adviser.
Protesters have defied police
warnings against demonstrations
They also threatened to halt all transport and cut communications in the area.
Mahmudur said on Sunday the violence had sent "negative signals" to Bangladesh's potential overseas investors and called for calm.
Trying to ease tensions, authorities on Monday withdrew police and paramilitary troop reinforcements from Phulbari, witnesses said.
The withdrawal cheered the protesters, who vowed to force Asia Energy out of the area.
Asia Energy intends to spend $3 billion on the mine and a related power plant.
Total investment over the mine's 30-year life is expected to total $10.4 billion.
Gary Lye, chief executive officer of Asia Energy Corporation (Bangladesh) Pty Ltd, denied the Phulbari project would harm people or the environment.
Asia Energy said it had submitted development plans and a feasibility study and was awaiting final government authorisation to start mining.