The parliament elected her as the country's first female president on Wednesday.
Congratulating Bhandari on her election to Nepal's highest position, president of India Pranab Mukherjee said he is confident that Nepal will move toward peace, stability and development under the guidance of Bhandari.
"India attaches the highest priority to further development of its close and multi-faceted relationship with Nepal," said Mukherjee in his official twitter handle. "As a close friend & neighbour, India will continue to extend all possible assistance & cooperation to Nepal."
China on the same occasion congratulated Bhandari.
"We hope the Nepalese people will work together to build a peaceful, stable and prosperous Nepal under the leadership of the president and the Nepalese government," said Chinese Foreign Ministry spokesman Lu Kang at a routine press briefing.
China supports Nepal's efforts to maintain national independence, sovereignty and territorial integrity, Lu said, adding that China will continue to provide assistance for Nepal's development.
In a statement issued by the White House on Thursday the United States congratulated the newly-elected prime minister KP Sharma Oli on his election as Prime Minister earlier this month and to Bhandari on her historic election as Nepal's first female President on Wednesday.
"These elections follow the promulgation of a constitution and the formation of a new government, milestones in Nepal's democratic development that demonstrate the people of Nepal's commitment to democracy," read the statement. "The United States looks forward to continuing to partner with the people and government of Nepal as they build a more unified, stable, and prosperous country and rebuild after the devastating earthquake and its aftershocks earlier this year."
Md Abdul Hamid, president of Bangladesh, expressed his confidence that Bhandari's long experience in public service will enable her to carry out her duties successfully.
He said Bangladesh greatly values its warm and excellent relationship with Nepal that is based on multitude of commonalities. "The support that the people and the political leadership of Nepal extended during our War of Liberation in 1971 is remembered by us all. I look forward to working closely with you to not only strengthen and deepen this strong friendship but also to promote our common interests in various arenas for benefit of the peoples of both the countries."
Hamid also invited Bhandari to visit Bangladesh at her earliest convenience.
Sheikh Hasina, prime minister of Bangladesh, describes Bhandari's election as a historic moment for all the women of South Asia as it reflects the political and social empowerment of women in this region.
"I am confident that together we would be able to further strengthen our bilateral ties and attain greater peace and progress for the entire region," said Hasina.
Bangladesh's GDP growth to overtake China, IMF report forecasts