He circulated his appeal through a video message posted on the website of a social media.
Tarique Rahman is BNP's Senior Vice Chairman and has been living in London since 2008.
He joined his mother in lambasting the government for trying to hold a 'farcical' election.
"The time has come for all of us to prevent and boycott the Jan 5 polls. Not for personal interest but for the sake of the country's existence," said Rahman.
The 18-party Opposition alliance led by the BNP has called a 48-hour nationwide strike from Saturday to thwart the poll.
Polling centres in different parts of the country have been set on fire since Friday night amid the Election Commission's preparations to hold voting in 147 constituencies.
The BNP leader described the ongoing agitation as one to 'restore democracy'. "A lot leaders-activists and general people have lost their lives in the movement to uphold democracy.
"The time has come to bury all differences to achieve one goal -- stop the farcical elections."
Calling upon the government to postpone the polls, Tarique said: "Sheikh Hasina had said that she would sacrifice the most. She wants peace, not Premiership. And the pre-requisite for that peace is to stop this election."
He also said that the Leader of the Opposition and BNP chairperson Khaleda Zia has been put under 'house arrest', an allegation the government has denied persistently.
"The two adversaries now are not the BNP and the Awami League or the alliances they lead. It is now a fight between democracy and autocracy, the force that upholds the interest of Bangladesh versus the force in favor of another country, the people's desire for freedom versus a ruler's desire to hold on to power."
He asked the people to decide on which side they were on.
"It's your decision, which side you will take judging the current situation. Our movement is for the non-party and neutral caretaker government which all of you believe is integral for a credible election. So, this is not only our movement but yours as well," said the Senior Vice Chairman of BNP.