West Indies decision to withdraw was prompted by an explosion near the team hotel in Chittagong Sunday as the country prepares for general election next month, reports CMC.
BCB president Nazmul Hassan says once the general election, carded for Jan 5, are held the violence is likely to dissipate.
"The impact won't be severe. The situation can't be like this all the time. We are hoping before the start of the World T20s, there will be a solution to our political situation," said Hassan.
"If there is no solution then the games won't be played, but by January all these solutions will come. So I am not worried about the World T20s. I am hopeful that all the instability will end in December."
The West Indies players and staff remained within the premises of Hotel Agrabad in central Chittagong, but are expected to move to Dhaka Tuesday.
The WICB had said Sunday that it was making arrangements for the players to leave the country, but the BCB wants to discuss resuming the tour with the WICB.
"Whether they (West Indies) are thinking about the future or worried about security now that the election is closer, I don't know," Hassan said.
"We will have a telephone conversation with the WICB officials."
The ongoing troubles in Bangladesh seemed to have escalated in recent months and the two main political parties have been at loggerheads.
However, Hassan has played down the impact of the West Indies Under-19 team's withdrawal from the tour on the country's hosting of the World Twenty20 in February.
"There is a bit of political instability, this has always happened, but I don't believe that we have reached a scenario where the games would be called off," said Hassan.