The West Bengal chief minister also told the Bangladesh prime minister on Saturday that the bill for implementing the Land Boundary Agreement between the two countries is likely to go through the next session of the Rajya Sabha (Upper House) of the Indian parliament starting end of this month.
Banerjee had stoutly opposed both the deals since 2011, arguing they go against the interests of West Bengal. But with changing Indian political realities, her stance on both has changed considerably.
So though she dropped out of erstwhile prime minister Manmohan Singh's entourage in 2011, Banerjee is now in Bangladesh with a large entourage of politicians and cultural personalities to join the International Mother Language Day.
This is her first visit to Dhaka after 17 years.
The prime minister's spokesperson Iqbal Sobhan Chowdhury told journalists Banerjee raised the Teesta issue during her meeting with Hasina at the Ganabhaban.
On Friday, she had told journalists she would raise the Teesta issue with her.
Though a solution to this vexed issue depends on Dhaka and Delhi, the role of the chief minister of a border state like West Bengal is believed to be crucial.
Mamata has already asked Bangladeshis to repose faith in her to deliver a settlement on the Teesta issue.
"Bangladesh has a problem, we also have problems but I will discuss this with Hasina-di (elder sister Hasina) and work out a solution," Mamata said on Friday.
"Mamata Banerjee has assured our prime minister of working out a solution that protects the interests of both West Bengal and Bangladesh," Sobhan Chowdhury said.
Banerjee has said that the relations of the two Bengals (Bangladesh and West Bengal) is as 'deep and durable' as perennial rivers Ganga and Jamuna.
The West Bengal chief minister was served the famed hilsha fish for lunch at the Ganabhaban.
Banerjee has raised the issue of Bangladeshi hilsha not being available in West Bengal during her meeting with Hasina.
Warmly greeting her, Hasina quipped: "You give us water, we will give you hilsha.”
Chowdhury said the relations between the two woman politicians resembled that between sisters – Banerjee being the younger one.
"I have settled all the problems arising out the 1974 Indira-Mujib pact. I hope that will be cleared in the next parliament session that begins on Feb 23," Banerjee told Hasina.
Hasina welcomed Mamata's support on the issue.
The prime minister reminded the West Bengal chief minister of the serious problems faced by those living in the enclaves, Chowdhury said.
Banerjee said she had herself seen the problems the residents of the enclaves faced.
Chowdhury said the officials of the two sides first met to discuss the contentious issues at the Ganabhaban.
Then Banerjee met Hasina exclusively for 30 minutes before lunch.
She told the prime minister she was in her teens during the 1971 Liberation War but was a regular listener of the Swadhin Bangla Betar (radio station of the Bangladesh government in exile).
She told Hasina that she felt truly honoured to be invited as a special guest for the Amar Ekushey (Immortal 21st) celebrations.
Mamata first met Hasina and exchanged pleasantries at the Central Shaheed Minar where both turned up to offer respects to the Language Movement martyrs.
On Friday, she met President Md Abdul Hamid and later visited the Bangabandhu Museum at Dhanmondi.