Rapid Action Battalion (RAB) spokespersons said they arrested Touhidur Rahman, 58, and two other "active members" of a group called Ansarullah Bangla Team (ABT), which was banned in May over a series of killings of bloggers.
"We've arrested them in the capital today. We can confirm that Rahman is a Bangladesh-origin British citizen. He is the main planner of the attacks on Avijit Roy and Ananta Bijoy Das," Major Maksudul Alam of the RAB told AFP.
Read: Fourth secular blogger hacked to death in Bangladesh
"He told us that he is a British citizen," said Mufti Mahmood, the head of the RAB's legal and media division, adding that the three would be paraded before the press later Tuesday.
Four secular bloggers have been hacked to death in Muslim-majority Bangladesh since the start of the year, including Roy and Das, prompting international condemnation and sparking protests mainly by secular activists in the capital.
Roy, a US citizen who was born in Bangladesh, was murdered in February by a gang wielding machetes in an attack in Dhaka. Roy's wife was badly wounded in the attack.
Das, 33, was killed in similar fashion as he headed to work at a bank in the northeastern city of Sylhet on May 13.
The government has vowed to hunt down the killers after facing accusations that too little was being done to stop such attacks.
Police described Rahman as the main planner of the attack as well as the "main financier" of ABT, whose members are mostly students from private universities.
"The other two Ansarullah members arrested today are Sadek Ali and Aminul Mollick. Ali has admitted in primary investigations that he took part in both the murders," Alam said.
Bangladesh police last week also arrested two suspected members of the group for the murder of Niloy Chakrabarti, who became the fourth blogger to be killed when he was hacked to death at his home on August 7.
Chakrabarti, who used the pen-name Niloy Neel, had posted on Facebook months before his death that he had been followed by two young men, but police refused to register the complaint and instead told him to leave the country.
Read: Bangladesh police arrest two over blogger murder
The other victim was 27-year-old secular blogger Washiqur Rahman, who was killed in Dhaka four months ago.
Most secular bloggers have gone into hiding, often using pseudonyms in their posts. And at least seven have fled abroad, according to a Canada-based atheist blogger Farid Ahmed who helped several of them.
Police were also investigating claims made by a third party that al Qaeda in the Indian Subcontinent (AQIS) was behind the killings. AQIS has already claimed responsibility for the murder of Roy.
In a recent petition to Prime Minister Sheikh Hasina, authors including Salman Rushdie and Margaret Atwood called on her government "to do all in their power to ensure that the tragic events... are not repeated".
Bangladesh is an officially secular country, but more than 90 percent of its 160 million people are Muslim.
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