The meeting received a cautious welcome from analysts who see it as another sign of improving ties between the countries
President Asif Ali Zardari on Sunday became the first Pakistani head of state since 2005 to visit India, on a one-day trip that he described as "very fruitful" in improving ties between the rivals.
During a visit billed as private but of great diplomatic significance, Zardari lunched with Indian Prime Minister Manmohan Singh and invited him to visit Pakistan.
The meeting has received a cautious welcome from analysts who see it as another sign of improving relations between the bitter neighbours, but the issue of Pakistani militant activity against India remains deeply problematic.
India continues to press Pakistan to prosecute the perpetrators of the 2008 Mumbai attacks, blamed on the militant group Lashkar-e-Taiba (Army of the Pure), which was founded by hardline Islamist Hafiz Saeed.
Saeed lives openly in Pakistan, where the government says it has insufficient evidence to prosecute him, but his terror links were highlighted recently by a $10-million bounty for his arrest offered by the United States.
"We have had some very fruitful bilateral talks together," Zardari said at a joint news conference during the first presidential trip to India since Pervez Musharraf visited seven years ago.
"We would like to have better relations with India. We spoke on all topics that we could," added Zardari, who was accompanied by a large delegation including his son and Interior Minister Rehman Malik.
The lunch -- with kebabs and curries from all over India, including the disputed region of Kashmir -- was preceded by a 40-minute private conversation between the two leaders.
"I am very satisfied with the outcome of this visit," Singh told reporters. "President Zardari has invited me to visit Pakistan and I'd be very happy to visit Pakistan at a mutually convenient date."
He stressed that relations between the countries "should become normal. That is our common desire."
Analysts had predicted little progress on sensitive topics such as Kashmir, which is divided but claimed in full by both countries, or the presence of anti-India militant groups in Pakistan.
Both were discussed, along with "the activities of Hafiz Saeed" and ways to increase trade between the countries, India's Foreign Secretary Ranjan Mathai told reporters.
A visa agreement that will simplify cross-border travel had been worked out and would be signed at a later date.
"Both felt that we need to move forward step by step," Mathai said of the talks between the leaders, which will be followed by meetings between home and trade ministers in the coming months.
India broke off a slow-moving peace process to settle all outstanding problems with Pakistan after the Mumbai attacks, which left 166 people dead, but the two sides have since warily returned to the table.
"This is a largely symbolic occasion and contentious subjects will be avoided," said Brahma Chellaney, an analyst at New Delhi's Centre for Policy Research, of the meeting Sunday.
Pakistan's foreign policy is seen by many observers as the preserve of the powerful military, and Chellaney suggested Zardari wielded little real power.
"You can't have substantive talks with someone who doesn't run anything," he said.
Zardari later flew to a Sufi shrine in the town of Ajmer, 350 kilometres (220 miles) southwest of New Delhi, where he offered prayers at the renowned complex of mosques built around a tomb commemorating a saint who died in 1236.
Sufism, a mystical and moderate branch of Islam popular in South Asia, has come under attack from hardline extremists in Pakistan who have launched attacks against worshippers and their shrines in recent years.
In Pakistan on Sunday, the government was dealing with the aftermath of a huge avalanche the day before which smashed into an army camp, burying up to 135 people, mostly soldiers, on the de facto border with India.
Pakistani troops were frantically trying to find signs of life in an area near the Siachen glacier, an inhospitable icefield that became the site of fierce fighting between Pakistan and India in 1987.
India and Pakistan have fought three wars since independence from British rule in 1947 and also carried out tit-for-tat nuclear tests in 1998.
They came to the brink of conflict most recently in 2001, and tensions again peaked after the Mumbai attacks.