Mr Karzai blamed the bombing on the "enemies" of the strong friendship between the two countries.
Both men reiterated their countries' enduring friendship and Mr Singh said the terrorist attack would not deter India helping Afghanistan.
41 people were killed and a 140 others injured, including two Indonesian diplomats, when a suicide bomber rammed his car into the gates of the Indian embassy.
Two Indian diplomats and two Indian guards were among the dead.
India has been one of the strongest allies of Afghanistan since the 2001 ouster of the hardline Taliban regime, providing essential resources for reconstruction including for roads, electricity and other infrastructure.
The Afghan government has often accused elements in Pakistan's army and its intelligence service of supporting the Taliban.
However it has not directly accused Pakistan this time.
Afghan Interior ministry spokesman Zemarai Bashary says regional intelligence networks are helping the investigation.
"Our intelligence department are saying that this attack is being conducted with the support of some intelligence network in the region," he said.
"I can't exactly say which but I can say yes some of the intelligence networks are involved in this".
Pakistan and the Taliban have denied involvement in the attack.