The talks were held at the Prime Minister House here before the luncheon reception, which was hosted for President Zardari by Indian Prime Minister Manmohan Singh.
Flanked by President Asif Ali Zardari and Chairman of the Pakistan People's Party Bilawal Bhutto-Zardari, Prime Minister Manmohan Singh, told newsmen after his half-an-hour-long one-on-one meeting: "President Zardari is on a private visit and I have taken advantage of this visit to discuss with him all bilateral issues. I am very satisfied with the outcome of this visit."
He said: "President Zardari has also invited me to visit Pakistan. I would be very happy to visit Pakistan on a mutually convenient date."
Dr Manmohan Singh said: "The relations between India and Pakistan should become normal. That is our common desire. We have a number of issues, and we are willing to find practical, pragmatic solutions to all those issues and that's the message that President Zardari and I would like to give."
Reciprocating the sentiments, President Asif Ali Zardari, told reporters: "I would like to wish the people of India Asalaamo Aalekum from the President of Pakistan." President Zardari said: "I'm grateful to Manmohan Singh, the Prime Minister of India, for inviting me for lunch although I'm on a private visit here. But we've had some fruitful bilateral talks together."
The President said: "India and Pakistan are neighbours. We can (and) we would like to have better relations with India."
He said: "We've spoken on all topics that we could have spoken about and we're hoping to meet on Pakistan's soil very soon."
Reuters adds: President Asif Ali Zardari and Indian Prime Minister Manmohan Singh stood together in New Delhi on Sunday, adding weight to peace efforts by the nuclear-armed foes with the first visit by a Pakistani head of state to India in seven years.
Relations have warmed since Pakistan promised its neighbour most favoured nation trade status last year, although a $10 million bounty offered by Washington for a Pakistani Islamist blamed for the 2008 attacks on Mumbai has stirred old grievances.
The leaders discussed Kashmir, theatre of two of three wars between India and Pakistan, as well as terrorism and trade during a 40-minute meeting on their own before sharing lunch, India's Foreign Secretary Rajan Mathai told reporters.
"We would like to have better relations with India. We have spoken on all topics that we could have spoken about and we are hoping to meet on Pakistani soil very soon," Zardari told a briefing as they emerged from Singh's residence.
Zardari then headed to the shrine in western India of a revered Sufi Muslim saint seen as a symbol of harmony between South Asia's often competing religions.
On his first visit to India as part of the 40-member delegation, Zardari's son, Bilawal Bhutto Zardari, stood behind the leaders, in a sign of his growing role in politics.
Mathai said Singh offered Zardari India's help in finding 124 Pakistani soldiers and 11 civilians engulfed by an avalanche on Saturday near the 6,000-metre-high (18,500-foot) Siachen glacier in Kashmir - known as the world's highest battlefield.
Zardari thanked Singh but did not immediately respond to the offer to help rescue teams, backed by helicopters and sniffer dogs combing an area one-km (half a mile) wide with snow up to 80 feet (25 metres) deep. Hundreds have died at Siachen over the years, mainly from the inhospitable conditions.
A foreign ministry source said the timing of any visit by Singh to Pakistan would depend on issues including a conflict over the oil-rich Sir Creek river estuary, one of their longest running disputes.
MUMBAI ATTACK
Singh told Zardari it was imperative to bring to justice the perpetrators of a 2008 attack on India's financial capital, Mumbai - a three-day gun and bomb rampage by 10 Pakistani militants that left 166 dead and derailed the peace process. Talks only resumed last year.
The Indian prime minister raised the continued freedom of Hafiz Saeed, the Islamist suspected of masterminding the attack. Saeed will be discussed again at a forthcoming meeting between home ministry officials, Mathai said.
India is furious Pakistan has not detained Saeed, despite handing over evidence against him. Pakistan Prime Minister Yousuf Raza Gilani said on Friday that anyone with concrete proof to prosecute Saeed should present it to the courts.
Relaxed visa rules will be signed at the same meeting of officials. Pakistan is expected to formally designate India as a most-favoured-nation later this year.
With Zardari and Singh both suffering major domestic problems, prospects are low for fixing the Kashmir stand-off.
Lasting Pakistan-India peace would go a long way to smoothing a perilous transition in Afghanistan as most NATO combat forces prepare to leave by the end of 2014.