Koirala apprised Krishna of the latest political developments and the continuing standoff between Prime Minister Nepal and Maoist chief Pushpa Kamal Dahal Prachanda over a host of issues.
The former guerrillas Monday vowed to keep up their siege on parliament - a move that could derail the promulgation of a new constitution next summer.
The Indian side emphasised the need to sign a new extradition treaty that could be useful in arresting criminals who cross the border and in curbing other cross-border criminal activities.
The expansion of economic ties figured prominently in Koirala's talks with Commerce and Industry Minister Anand Sharma and Home Minister P. Chidambaram.
Koirala made a strong pitch for greater Indian investment in the Himalayan state.
This is the first visit to India by Koirala, the daughter of five-time former Nepali prime minister Girija Prasad Koirala, since she became foreign minister.