Roadworthiness rules will be used to enforce the decision, he said.
"The transport minister passed the order to give the two cities a better image during the World Cup.
A lot of tourists will visit Bangladesh at that time and we want to show them the best face of our cities," he said.
Mobile courts led by magistrates will hit the roads to hand out instant punishment to errant owners, he said, adding "there is no way old, worn-out and clunky vehicles will be allowed to move.
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Cricket-mad Bangladesh is a co-host of the World Cup, which starts February 19, and Dhaka is keen to present a new image of the poverty-stricken country during the six-week long competition.
"As part of the sprucing up drive, state-owned buses will be painted with faces of its national cricketers, monuments and tourism spots," Naser said.