Bangladesh team manager Khaled Mashud says they were 50 yards away from the Al Noor mosque in Christchurch when a gunman entered and killed 41 people.
The Bangladesh team were planning to visit the mosque before the start of their third Test against New Zealand, which was due to begin in Christchurch at the Hagley Oval on Saturday.
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None of the Bangladesh players or staff were injured, but Mashud said: "We were very close to the mosque, and we could see from the bus. We must have been about 50 yards from the mosque.
"I would say we were really lucky. Had we reached even three or four minutes earlier, we probably would have been inside the mosque.
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"This could then have been a massive incident. We are very thankful that we weren't caught in the crossfire, but what we saw was straight out of a movie scene. We could see bloodstained people staggering out of the mosque.
"Maybe in about eight to 10 minutes, we were all inside the bus and were sitting with our heads bowed, just in case someone fires at us."
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The decision to call off the final Test was made after New Zealand Cricket chief executive David White spoke to his Bangladeshi counterpart.
Arrangements are now being made for the Bangladesh team to return home as soon as possible.
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Jacinda Ardern, the Prime Minister of New Zealand, confirmed 49 people were killed during the attacks. Two mosques were targeted, with the deadliest attack taking place at the Al Noor mosque in the city centre.
Three men and one woman were held in custody following the attacks, while a number of improvised explosive devices strapped to vehicles were made safe by police. One male has since been charged with murder.