The two leaders met in the Rashtrapati Bhavan, a statement said.
Greeting the Liberian president at a banquet hosted in her honour Wednesday night, Mukherjee said Sirleaf's visit was "an occasion for us to celebrate the centuries-old relationship between India and African nations".
"India believes that its experience could be of relevance to Liberia's socio-economic development. India's development partnership with Liberia will respond to Liberia's requirements as it chooses its priorities and options - and forges its independent path of advancement and growth," said Mukherjee.
Liberia, bordered by Sierra Leone to its west, Guinea to its north and Ivory Coast to its east, is home to about 3.7 million people and exports natural resources such as iron ore, rubber and timber.
Welcoming the Liberian president on her first state visit to India, President Mukherjee said "her steadfast determination and inspiring leadership has helped Liberia become a land of opportunity", a statement issued here Thursday said.
"She has dramatically altered the course for Liberia, and is a guiding light and an example of women's leadership that will inspire communities and nations not only in Africa, but across the globe."
Mukherjee said: "India sees the Africa of today as a continent that is illuminated by the freedom, optimism and confidence that its people have in the power of their own potential.
"Guided by the wisdom of their ancestors, enthused by the vigour of their young generations, sustained by their rich diversity and natural resources and inspired by the vast horizons opening up to them, there is no limit to what Africans can achieve in terms of progress and prosperity."
He said the African continent "is today at a threshold, embarking on a path of sustained growth and poised to play a defining role on the world stage".
President Sirleaf is on a five-day state visit to India Sep 9-13.
--IANS (Posted on 12-09-2013)