"We have found out that he was trying to set up contact with IS and al-Nusra Front," a Bangladesh police spokesman said identifying him as Samiun Rahman aka Ibn Hamdan.
Police said he had admitted trying to recruit militants for the fanatical Islamist group responsible for the murder of thousands of people and the beheadings of at least three Westerners.
His arrest came two days after the police said they were looking for an "al-Qaeda operative" British citizen while he was now in Dhaka to recruit fighters for the IS.
Police said it was not yet clear whether Rahman, of Holborn in central London, had succeeded in recruiting militants to join IS fanatics in Iraq and Syria.
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Rahman was born in the UK to Bangladeshi parents and, according to neighbours, converted to Islam during a prison term, 'Evening Standard' said in a report.
Police said Rahman had connected with a young man in Bangladesh via Facebook before arriving in the country.
Last Wednesday, police arrested two youths, who are in their 20s, alleging that they were trying to go to Syria via Turkey with the help of a British citizen posing as members of Tabligh Jamaat, a peaceful movement for spreading Islam.
One of the youths is a son of a retired judge while the father of another is a senior government official whose names police did not disclose.
On the very next day, they nabbed a 22-year old man Hafizur Rahman alleged to be a ring leader of an international terror outfit that recruits Jihadis from across the world.