Karzai is expected to discuss another ambitious gas pipeline project - worth $3.3 billion - with Indian leaders during his three-day visit.
The project envisages a pipeline running from Turkmenistan to Pakistan and eventually on to energy-hungry India.
India, with its robust economy and fast-growing energy needs, is the focus of regional efforts to build gas pipelines across several nations.
On Tuesday, energy-surplus Iran and Pakistan further pushed a long talked-about $4-billion pipeline project that runs from the Gulf nation through Pakistani soil into India.
Pakistan's Prime Minister Shaukat Aziz went to Tehran with high expectations of "substantial progress" on the scheme, while Iran's Foreign Minister Kamal Kharrazi was in New Delhi to overcome Indian reservations.
Kharrazi (R) is trying to
overcome India's reservations
"We are convinced that the Iran-India pipeline through Pakistan will benefit all three countries and substantially improve political and economic relations between India and Pakistan," Kharrazi told a foreign policy thinktank in New Delhi on Tuesday.
A memorandum of understanding was expected to be signed but the statement of cooperation that was released by the Indian Foreign Ministry only referred to improving cultural relations between India and Iran.
But New Delhi indicated its growing interest in the proposed Iran-Pakistan-India pipeline on Tuesday with its Foreign Ministry saying an Indian petroleum ministry technical team would visit Iran in late February to discuss the project's feasibility.
A pipeline would earn Pakistan millions of dollars from transit fees, but more importantly, it will create an economic bond with neighbouring India, with which it has fought three wars.
During talks in Islamabad last week to push along a year-old peace process, India signalled it was willing "to look at" the project, dubbed "the peace pipeline", subject to security considerations.
"Our effort is that Iran, Pakistan and India should take this project forward"
Pakistani prime minister
Pakistan's Aziz, who is also finance minister, has championed the need for stronger economic ties with India to normalise relations, and was upbeat as he headed to Iran.
"In my view, there will be substantial progress on the gas pipeline project during this trip," he told state television in Islamabad before leaving on a three-day visit.
"Our effort is that Iran, Pakistan and India should take this project forward. Our energy needs are increasing and if we get gas from abroad, it will benefit the economy," said Aziz.
Although India is looking at the Turkmen and the Iranian projects, some analysts say a link from Myanmar via neighbouring Bangladesh is also possible.