The Tigers are scheduled for three fixtures in Kolkata and one in Mumbai at the global tournament that starts on 7 February.
The issue started when Bangladesh seamer Mustafizur Rahman was withdrawn from IPL Kolkata Knight Riders on the instruction from the BCCI.
Political relations between the two countries have deteriorated in recent months and the Bangladesh government then banned the broadcast of the IPL in the country following Mustafizur's withdrawal.
The ICC shared a security assessment which indicated no specific threat to the Bangladesh team in India but the BCB will remain firm in it's stance.
In a statement the BCB said: "During the discussions, the BCB reaffirmed its position regarding the decision not to travel to India, citing security concerns.
"The board also reiterated its request for the ICC to consider relocating Bangladesh's matches outside India.
"While the ICC highlighted that the tournament itinerary has already been announced and requested the BCB to reconsider its stance, the board's position remains unchanged.
"Both parties agreed that discussions will continue to explore possible solutions. The BCB remains committed to safeguarding the well-being of its players, officials and staff while engaging constructively with the ICC to address the matter."
The ICC has said there is no specific or heightened security threat for Bangladesh playing in India at the T20 World Cup, even though the country's sports adviser said they still have concerns.
Bangladesh batter Najmul Hossain Shanto admits "it is not easy" to perform in global tournaments when off-field controversies continue to haunt the team.
Ross Adair has recovered from injury and has been included in Ireland's squad, that will be captained by Paul Stirling, for the upcoming T20 World Cup that kicks off on 7 February.
The Bangladesh Cricket Board (BCB) says the ICC "has conveyed its willingness to work closely" with the country due to security concerns about playing in India at the T20 World Cup.
