According to The Express Tribune, PCB chairman Shahryar Khan wrote in the letter that Anurag Thakur, secretary BCCI, should make the series possible in December.
The BCCI had signed an MOU to play Pakistan in six series between 2015 and 2023, with the first to be hosted by the PCB in the UAE in December.
However, the two boards differed over television broadcast rights and India have been reluctant to discuss the series due to the recent cross-border terrorism.
"Cricket is a tool to formulate peace between the countries."
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Officials from both the boards have been doing some tough talking in the last few weeks.
While Khan had said that Pakistan can survive without playing India, Thakur had made it clear that 'bullets and cricket' can't go together.
Infact, after reports emerged that wanted terrorist Dawood Ibrahim was in Karachi, Thakur had written in his twitter handle: "Dawood in Karachi. NSA wants to meet separatists here. Are you really serious about peace and you expect we'll play cricket with you?"