Modi expressed hopes that it will be possible to 'settle' the issues 'soon' during a meeting with the Bangladesh president at New Delhi's Hyderabad House on Friday.
The leaders spoke about bilateral issues in the meet that lasted about half an hour.
President Hamid expressed gratitude for India's support during the 1971 Liberation War. He also praised Modi's leadership, said the president's Press Secretary Ihsanul Karim after the meeting.
"Referring to the Gujrat model in the development of India, the president told Modi that it will help accelerate India's progress and that the young generation has faith in him."
Hamid hoped that Modi's government would soon iron out the thorny issues of Teesta signing and Land Boundary Agreement.
"The Indian prime minister replied that his government is working on settling the issues. He is hoping they'll soon be settled."
Earlier, Modi assured his Bangladesh counterpart Sheikh Hasina of settling the matters at the 18th SAARC summit at Kathmandu towards the end of November.
He went to Assam, where the Land Boundary Agreement is strongly opposed, and pitched for the agreement with Bangladesh, saying the land swap deal would benefit Assam in the long run.
India signed the LBA to facilitate the exchange of the enclaves in 2011 during former prime minister Manmohan Singh's visit to Dhaka.
West Bengal Chief Minister Mamata Banerjee has been sternly opposing the exchange but recently signalled a change of heart.
The president also asked for cooperation in taking the hydro-electricity generated in Nepal and Bhutan through India to Bangladesh, said Ihsanul Karim.
"Both of them underlined the need for increasing regional connectivity in the meeting. Narendra Modi said working towards development in infrastructure and regional cooperation will benefit everyone."
The Indian prime minister also put emphasis on cooperation in tourism, said the press secretary.
"He told the president that both his meetings with Prime Minister Sheikh Hasina in the United States and Nepal have been productive. He has also stressed on working together to control narcotics."