Ms Espinosa is only the fourth woman to be president of the Assembly — a position held by 69 men through the UN’s history.
Vijaya Lakshmi Pandit, who was Jawaharlal Nehru’s sister, was elected Assembly President in 1953.
The MPs who met her represented a cross-section of India’s political parties and geography and are members of India’s delegation to the Assembly.
Mr Rai said that Ms Espinosa, who is from Ecuador, told them that she respects Indian democracy and considered India a country from which to draw inspiration, pointing to a book on Mahatma Gandhi in her office.
After Vijaya Lakshmi Pandit it took 16 years for another woman, Angie Elisabeth Brooks of Liberia, to become Assembly President in 1969, and 37 more years before Sheikha Haya Rashed Al Khalifa of Bahrain was elected in 2006.
Developing countries produced all the four women presidents.