After meeting Cricket Australia (CA) officials in Dhaka, Home Minister Asaduzzaman Khan said the Aussies would get security usually reserved for visiting heads of state if they went ahead with the tour starting this week.
"The highest security protocol will be provided for the Australian cricket team," Khan told reporters.
Bangladesh Cricket Board (BCB) president Nazmul Hassan said the Australian foreign ministry's advice to delay the team's departure on Sunday "has shocked me".
Australia are now booked on a flight to Bangladesh late Tuesday but will await security briefings over fears militants could target Australians before deciding whether to go ahead.
Also Read
CA's anti-corruption and security manager Sean Carroll and two other Australian officials met top security and intelligence figures in Dhaka on Monday, along with home minister Khan and BCB chief Hassan, Dhaka cricket officials said.
Sunday's planned departure was blocked after the foreign affairs ministry in Canberra warned that "militants may be planning to target Australian interests".
"Today is a big day, we have a lot of meetings, a lot of people on the ground. We want to make sure we are not under-reacting, but also not over-reacting."
"The advice we got was pretty direct against Australians and we want to make sure we're doing our due diligence.
"We've bought ourselves 72 hours, but Cricket Australia is not going to put the players at risk."
He added that there was no specific threat against the Australian side.
Bangladesh are scheduled to host Australia for the first Test from October 9-13 in Chittagong and the second from October 17-21 in Dhaka. A three-day warm-up match was set to start on October 3 in Fatullah.