With her younger son Arafat Rahman detained in the early hours of Monday, former Bangladesh prime minister Khaleda Zia was under increased pressure to quit the country.
Arafat, the relatively low-profile businessman son of Zia, was detained at 1 am.
His elder brother Tareq Rahman, an office bearer of the Bangladesh Nationalist Party (BNP), has been in jail since March 7.
Arafat was picked up when he had gone to his mother's residence late Sunday and held prolonged negotiations with security forces.
Zia was allegedly asked by the officers to quit the country to avoid further problems, but she refused, saying she was "ready to face consequences", New Age newspaper said.
The government of Chief Advisor Fakhruddin Ahmed, widely perceived as being "army-backed", has denied any plan or move to "force" Zia and her principal rival and former prime minister, Sheikh Hasina, to leave the country.
Unlike Tareq's prolonged haggling before being taken away, there appeared nothing dramatic about Arafat's detention. Security forces "sped him away" after his detention, the paper said.
There were protests by BNP workers when Tareq was detained. The caretaker government has imposed a blanket ban on political activity.
A national emergency is in force since January 11, the day general elections were called off amid political turmoil.
Arafat runs a navigation company and an advertising firm that has the monopoly over billboards that abound in Dhaka.
His offices were raided twice last month and Arafat was placed "virtually under house arrest".
Harris Choudhury, who was Zia's political secretary when she was the country's prime minister (2001-October 2006), has also been detained and is under prosecution. The Daily Star said his offices were raided on Sunday.
Also remanded to police custody was Moudud Ahmed, lawyer-writer and a veteran of Bangladesh politics who was Zia's law minister.
Former ministers and lawmakers of Zia's BNP top the list of 50-plus high profile politicians and businessmen detained as part of the government's current drive against crime, corruption and religious extremism that has seen over 45,000 people detained and prosecuted.
Charges of extortion and murder have been slapped against Hasina as well. She is in Florida, the US, with her family and has vehemently protested.
Terming the extortion case against Hasina as "peculiar", Law and Information Adviser Mainul Hosein has said that the government would examine the case and take action "only if the allegations are proved to be true".
"Why will such a case be filed against a former prime minister? Rather, it should have been a corruption case," the law adviser said, adding that due to this oddity the national task force will examine the allegation. He was speaking at the BBC Bangladesh Sanglap on Saturday.