Security forces in both India and Afghanistan are battling Islamic militants who are allegedly backed by Pakistan, which lies between them.
Karzai and Singh also called for closer ties between the three countries to boost trade. India and Afghanistan have long urged Pakistan to open up a trade corridor through its territory, which would also speed the delivery of much-needed Indian aid.
Pakistan has, however, linked this to the resolution of the Kashmir dispute.
President Hamid Karzai and Prime Minister Manmohan Singh inspect a guard of honour in Kabul after the latter's arrival in Kabul on a two day visit Sunday
Text: Daniel Cooney, AP | Photograph: SHAH MARAI/AFP/Getty Images