Kabul's overtures to New Delhi are likely to rile Islamabad, where a new government led by two-time Prime Minister Nawaz Sharif is set to take office soon, promising improved ties with India.Pakistan has long resisted Indian involvement in Afghanistan, seeing it as a plan to encircle it, and any fresh wrangling between the rivals would add to Afghanistan's problems as the Western military withdrawal draws near.
Meanwhile, Karzai wants India to increase military aid to Afghanistan.
The two countries have already been cooperating in a number of ways. India has been training small numbers of Afghan officers at its military academies for years. And in 2011, New Delhi signed a strategic partnership with Kabul that will increase joint training once NATO troops leave Afghanistan in 2014. Officials say a deal to buy Indian artillery and aircraft is up for discussion on this trip.
India has already invested heavily in Afghanistan's civilian infrastructure. It has spent $2bn to build infrastructure such as roads, hospitals and electricity projects.
Karzai's visit to India comes at a time when Afghanistan's relations with neighbouring Pakistan appear to be deteriorating.