Ban telephoned Hasina in the morning and followed up with a call to Zia, the leader of the main opposition Bangladesh Nationalist Party, in the evening.
The impasse over electoral reforms figured in Ban's conversation with Hasina, the premier's press adviser Iqbal Sobhan Chowdhury told PTI.
Bangladesh's two main parties are divided on the issue of whether the next polls should be held under a caretaker regime. The BNP is pushing a proposal to reintroduce the system of a caretaker government that was abolished when Hasina's Awami League came to power in 2009.
Ban discussed various issues related to the next general election, expected to be held sometime between October and January.
Hasina told Ban that she wants a peaceful negotiated settlement of the crisis over poll reforms.
"Our Prime Minister assured the UN Secretary General that her government believes in peaceful settlement of the dispute through negotiations (with the opposition) to continue the democratic process as they talked for around 30 minutes," Chowdhury said.
Hasina told Ban the BNP was welcome to float its proposal for an amended electoral system during the upcoming parliament session next month.
The UN chief also spoke to BNP chairperson Zia for 30 minutes, her special assistant Shimul Biswas told the media without giving details.
BNP spokesman Mirza Fakhrul Islam Alamgir said details of the conversation would be disclosed at a press conference later.