"Awami League government had worked with five different governments of India from 1996-2001 and 2009-14 by maintaining good relations and solving many problems," she told a press conference in comments about the future of Dhaka-Delhi ties after the new Indian government came to power.
She added, "We must have exchange of visits. Problems will exist and those would be solved through discussion. Our policy is friendship to all, malice to none," she said.
Hasina said Awami League had worked with all Congress-led and non-Congress governments in India and had resolved several outstanding issues like the landmark 1996 Ganges Water Treaty.
She said she expected Modi to visit Bangladesh first as "I invited him first to visit Bangladesh".
The Bangladesh premier, however, again criticised West Bengal Chief Minister Mamata Banerjee for scuttling a proposed treaty for the sharing of waters of the Teesta river.
"We nearly inked the Teesta agreement, but it was not done due to the veto of West Bengal Chief Minister Mamata Banerjee at the last moment. Despite that we took the deal far ahead," she said.
But she said talks were underway to resolve the Teesta issue "though the responsibility of resolving the issue now lies with India".
However, she said, Bangladesh was now thinking about "alternative steps" for enhanced augmentation of flows in common rivers through initiatives like dredging.
The Bangladesh premier claimed her government took initiatives to solve land boundary problems with India and "Bangladesh has already ratified the Land Boundary Agreement, while India has placed the deal before its parliament. And I have firm belief that we could solve the problems".
"India is a large country and Bangladesh may be a small one, but we are independent and sovereign. All will have to keep this in mind," she said.
Hasina had earlier congratulated Modi on the resounding victory of his BJP-led National Democratic Alliance (NDA) in the Lok Sabha elections.
"I am delighted to see a great friend of Bangladesh leading an extremely friendly country, India, in the coming days," she said in a message sent to Modi while she later spoke to him on the phone.
At the time Hasina also told Modi "I hope that you would find my country your second home and first destination for your official visit abroad" while she praised his "dynamic, inspiring and visionary leadership qualities".