Touhidur Rahman, 58, and two active members of outlawed Islamist group Ansarullah Bangla Team were arrested in Dhaka on Monday night, said Maksudul Alam, a spokesman for the Rapid Action Battalion force.
“Rahman is a Bangladeshi origin British citizen and we suspect he is the main planner of the killings of US blogger Avijit Roy and Ananta Bijoy Das,” he told Reuters.
In February, Roy, an American citizen of Bangladeshi origin who was a critic of religious militancy, was killed with a machete, while his wife and fellow blogger, Rafida Bonya Ahmed, was seriously injured.
In May, the Indian-born head of al-Qaeda in the Indian subcontinent, claimed responsibility for a series of attacks in Bangladesh and Pakistan, including the death of Roy.
Das, another secular blogger, was also hacked to death with a machete in May. Two other bloggers, Washiqur Rahman and Niloy Chatterjee, suffered a similar fate.
Militants have targeted secularist writers in Bangladesh in recent years, while the government has tried to crack down on hardline Islamist groups seeking to turn the country into a sharia-based state.
Last week, police arrested two members of Ansarullah Bangla Team for alleged involvement in Chatterjee’s murder on 7 Aug.
Rahman, who was killed in March, had spoken out against Roy’s death on social media.
A Foreign Office spokeswoman said: “We are aware of reports that a British national has been arrested in Bangladesh and are seeking clarification from the authorities. We stand ready to provide consular assistance.”