"Metropolitan Magistrate Shahriar Mahmud Adnan granted us seven days to quiz them in custody," a police official told PTI.
The three, arrested in connection with the murders of Avijit Roy and Ananta Bijoy Das, are linked to the Islamist group Ansarullah Bangla Team which was banned in May over a series of killings of bloggers.
One of the suspects -- Tawhidur Rahman -- was the mastermind of the two murders.
Rahman is a Bangladesh-born British national who lived in London for more than two decades until 2011.
Roy, 45, a Bangladesh-born US citizen, was hacked to death on a street near an annual book fair venue in the capital in February this year while 33-year-old Das was killed in northeastern Sylhet in May.
They were known for their tough stance against religion-based politics and were linked to a platform which waged a massive campaign for the capital punishment for war criminals who carried out atrocities siding with the Pakistani troops in the 1971 liberation war.
Bangladesh police last week arrested two suspects in connection with the murder of another secular blogger Niloy Neel, the fourth blogger to be killed this year after the murders of Roy, Das and Washiqur Rahman.
"We now believe (Bangladeshi British) Tawhidur Rahman is also involved in the 2013 killing of Ahmed Rajib, the first of the seven bloggers who have been targeted by the militants," a RAB official said.
Ansarullah Bangla Team, also known as Ansar-Al-Islam, has claimed responsibility for most of the bloggers' murders. The group identifies itself as Bangladesh chapter of al-Qaeda in the Indian sub-continent.
The US as well as other nations have condemned the spate of killing of bloggers as cowardly acts and underlined the need to work together to counter violent extremism.