The Zimbabweans arrived in the Bangladesh capital on Monday to play three one-day internationals and two Twenty20 matches against the hosts.
Zimbabwe agreed to bring forward the series from January 2016 after Australia cancelled their tour in late September over official warnings that militants might attack Western interests.
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"We will play cricket and those who are qualified to look at these things (security issues) will do their job. They have given us the go-ahead to play here," captain Elton Chigumbura told reporters.
Zimbabwe is the first international team to arrive in Bangladesh since South Africa in August.
Bangladesh is desperate to avoid the fate of Pakistan which has had to host nearly all of its home matches at neutral venues since gunmen attacked the Sri Lankan team bus during a 2009 Test match in Lahore.
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Tension rose in Bangladesh after an Italian aid worker and a Japanese farmer were murdered last month in attacks claimed by the Islamic State. The government says the jihadist group has no presence in the country.
Apart from the Australian men, the South African women also cancelled their trip, just a day before they were due to arrive on Tuesday.
Zimbabwe coach Dav Whatmore, who coached the Bangladesh team from 2004-07, said his players have no issue with security.
"They (Zimbabwe Cricket) will never put us in a situation where we are compromised," said Whatmore.
Whatmore praised his former charges, saying the series will be challenging for fellow minnows Zimbabwe.
"Bangladesh had a good World Cup, making it to the quarterfinal. They have followed it up with some memorable wins here," said Whatmore.
"We know who we are up against. They are a good side."
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