An Indian foreign ministry source confirmed that Karzai had held talks late Tuesday with Prime Minister Manmohan Singh after a separate meeting earlier in the evening with his Indian counterpart Pranab Mukherjee.
But there were no immediate details about the discussions and officials said there would be no official statement as is customary after such meetings nor any plans for a press conference.
Officials had said before the meeting that Karazai would use his trip to India to drum up support from a long-time ally.
Karzai's spokesperson, Aimal Faizi, said last week that Karzai would ask for "all kinds of assistance from India in order to strengthen our military and security institutions" during his talks in the capital New Delhi.
An Indian foreign ministry official, speaking on condition of anonymity, also said at the weekend that the discussions would cover a potential arms deal between the two countries.
"India is ready to meet any request that would strengthen Afghan security institutions," said the official.
India has been training a limited number of Afghan military officers for years at its military institutions, but has provided little weapons assistance except for some vehicles.
Speaking on Monday night as he accepted an honorary degree from a university in the northern state of Punjab, Karzai thanked India for its support since he came to power in 2001 after the fall of the Taliban.
"India, as a friend of Afghanistan, has made an immense contribution in uplifting its youths," he said.
"India has contributed $2 billion from the hard-earned money of its taxpayers for the betterment of Afghanistan."
India's support for Karzai is a reflection of its desire to ensure that the departure of the United States and other foreign forces in 2014 does not lead to the return of the radical Islamist Taliban to power in Kabul.
The two countries are attempting to step up their already solid relationship before international troops leave Afghanistan in 2014, foreign policy expert Brahma Chellaney told AFP.
But any extra aid from India will be in the form of "indirect security assistance" such as more training of security officers and transfer of technology, said Chellaney, strategic studies professor at New Delhi's Centre for Policy Research, a think-tank.
"This (Karzai's visit) is part of a more intense interaction between the two countries before 2014," he said. "(But) there is no intention for India to have boots on the ground there."
In 2011, India and Afghanistan began a "strategic partnership" to deepen security and economic links. But Indian activity in Afghanistan has triggered unease in neighbouring rival Pakistan, which fears losing influence in Afghanistan.
India has been notably cool about US-backed attempts to negotiate a peace settlement with Taliban elements.
Speaking on a visit to Washington in February, Indian Foreign Secretary Ranjan Mathai said New Delhi saw little "dividing line" between al Qaeda and other militants.
Karzai is a regular visitor to India and spent time as a student in the northern resort city of Shimla. He was last in New Delhi in November when he told Indian business leaders that Afghanistan was ripe for investment and promised them a "red carpet welcome".
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Sir, keep yourself abreast of the news! Here the west is speaking about cutting off all aid to Karzai because the payoffs by the CIA and corruption (you may find related news on this very website) and there you are gladly wasting your income tax.
Save your money for the 400 million Indians who live below the poverty line. Half of the world's hungry and infant mortality cases are in India. Why must we always fight. Put your money to better use.
Now i will not feel bad while paying my Income Tax.