Karzai, who is on a two-day visit, was accorded a ceremonial welcome by Pratibha Patil, the Indian president, before his meeting with Singh.
India is currently involved in training Afghanistan's police and diplomats, building roads and hospitals, and supporting trade and services as the country tries to rebuild its economy, despite continuing Taliban attacks.
General Ravi Sawhney, a former Indian military intelligence official, told Al Jazeera that India has been very active in making sure "the maximum aid for reconstruction and rebuilding the battered and bruised country" was given.
"Now it is time that we also thought about giving some sort of aid for training their armed forces, because that is what is lacking," Sawhney said.
"The troops contributed by the Americans and Nato are not adequate. Not
enough attention has been paid to raising the [skills of] Afghan forces."
The aid increase comes a month after the Indian embassy in Kabul was hit by a major suicide attack that New Delhi blamed on regional rival Pakistan.
The July 7 embassy attack that killed 58 people, including India's military attache and a diplomat, "has tragically shown that terrorism has no barriers and is not bound by restraints", Singh said on Monday.
"It was an attack on the friendship between India and Afghanistan."
Afghanistan, India and the US have accused Pakistan's spy agency ISI of being involved in the attack.
Pakistan denies any involvement.