The talks cover security cooperation, investment, enhanced trade, power and energy sector cooperation, water sharing, Rohingya issue, border management, drug smuggling and human trafficking among others.
The two South Asian neighbours will also discuss further economic cooperation in the backdrop of the global economic downturn and the Russia-Ukraine war.
The two Prime Ministers earlier had an informal discussion.
After bilateral talks, Dhaka and Delhi are likely to sign several deals and MoUs on water management, railways, science and technology as well as information and broadcasting.
Earlier, Sheikh Hasina visited the Rashtrapati Bhavan where she was received by Modi at a ceremonial reception
The visiting leader later visited Rajghat to pay tribute to Mahatma Gandhi.
On her first day of India visit, Indian External Affairs Minister Dr S. Jaishankar called on Sheikh Hasina.
She then visited the Nizamuddin Aulia's Dargah and offered prayers. Later, Adani Group Chairman Gautam Adani paid a courtesy call on Sheikh Hasina.
The Bangladesh Premier is expected to address a meeting with top business leaders and attend a ceremony to award "Mujib Scholarship" to descendants of soldiers and officers of Indian soldiers who were killed or critically wounded during the 1971 war.
She will visit Khwaja Gharib Nawaz Dargah Sharif at Ajmer before returning to Dhaka on Sept 8.