This is Mr Karzai's second visit to India in the last six months.
India is the first country to sign a strategic agreement with Afghanistan in 2011. But so far, it has only agreed to train Afghan officers and cadets in specialised military institutions.
Mr Karzai is also expected to discuss recent skirmishes with Pakistan along the Durand Line, which Kabul has never recognised as the international border.
Each side has been accusing the other of firing across the mountainous border region for months, including a cross-border clash earlier this month that killed an Afghan border policeman.
Both countries have also accused each other of providing shelter for insurgents fighting on the other side of the border. Afghanistan's accusations that Pakistan is allegedly trying to torpedo efforts to start peace talks with the Taliban have also contributed to deteriorating relations.
Mr Karzai, who arrived in Punjab yesterday on the first leg of his tour of the country, was conferred an honorary doctorate degree by President Pranab Mukherjee in Phagwara.
India has invested more than US $2 billion in Afghan infrastructure, including highways and hospitals and rural electricity projects.
New Delhi is hoping to gain some influence in the country after 2014, when Western troops exit Afghanistan completely and Afghan forces become responsible for the country's security.