Yadav is on a brief state visit to India.
He and Shinde discussed a wide range of bilateral issues and also modalities on strengthening New Delhi’s ties with Kathmandu.
India’s foreign secretary, Rajan Mathai also met the visiting Nepalese President.
During his visit, Yadav met his Indian counterpart, Pranab Mukherjee and India’s Foreign Minister Salman Khurshid.
He also held delegation-level talks with Prime Minister Manmohan Singh during the day.
Nepal has been in a political crisis since May when a special Constituent Assembly missed a deadline to prepare a new constitution amid a political row over the number and names of the federal states to be created under the new system.
Earlier on Tuesday (December 25), the famed Banaras Hindu University (BHU) located in the temple city of Varanasi in northern state of Uttar Pradesh conferred an honorary doctorate on Yadav.
The degree was conferred by the erudite Indian lawmaker and former diplomat Karan Singh at the university’s convocation in President Pranab Mukherjee’s presence.
India is walking a diplomatic tightrope, as they are aware that excessive meddling in its traditional ‘backyard’ could risk pushing the fragile Himalayan democracy closer to China.
India has also nervously watched China’s rapid inroads into Nepal with plans of a rail service from Lhasa to the Nepal border.
Chinese interest in Nepal mainly centres on containing pro-Tibet politics. The battle is also for control of key passes in the Himalayas used by Tibetan separatists to go to India.
India and China fought a border war in 1962, but there is little possibility of an India-China proxy war in Nepal.
Landlocked Nepal depends on India for trade and crucial supplies of food and fuel. The two nations share a Hindu culture and many Nepalis cross over the border to work in India.
Trade and travel links across the Himalayas that divide Nepal and China are, by contrast, much weaker.