Puri met Prachanda at the Prime Minister's official residence Baluwatar in Kathmandu.
They discussed an "entire gamut of extensive bilateral ties between India and Nepal," an Indian embassy source said.
Prachanda congratulated the newly-appointed envoy and said his tenure would strengthen the ties between Nepal and India.
Puri said he would work to ensure cordial relationship is maintained and bilateral ties get a boost during his tenure.
Puri, a 1982 batch IFS officer, was on March 10 appointed as India's 24th ambassador to Nepal. His predecessor Ranjit Rae completed his three and a half year tenure on February 28.
Puri arrived in Kathmandu on Saturday and presented his credentials to President Bidya Devi Bhandari at a ceremony the next day.