New Delhi (CNN) -- Pakistan's President Asif Ali Zardari met with the Indian prime minister in New Delhi on Sunday -- the first visit to India by a Pakistani head of state in seven years.
Both leaders described their brief meeting as satisfactory, with Zardari extending an invitation to Prime Minister Manmohan Singhfor a reciprocal visit.
"I would be very happy to visit Pakistan on a mutually convenient date," Singh said after hosting Zardari at his official residence.
Emerging out of their almost 30-minute meeting on Sunday, Singh and Zardari said their talks covered all bilateral issues between their countries.
"I am very satisfied with the outcome of talks," Singh remarked as the Pakistani leader stood beside him.
He said both nations were willing to find "practical and pragmatic" solutions to issues between them.
Zardari echoed Singh's comments, saying their talks were "fruitful."
"We would like to have better relations with India. Hoping to meet (prime minister Manmohan Singh) on Pakistani soil very soon," he added.
Zardari's India visit came amid thawing relations between the two nuclear-armed nations.
After his talks with Singh, the Pakistani leader travels to the shrine of a revered Sufi saint at Ajmer in Rajasthan state.
The private tour comes in the wake of Pakistan's recent promise to grant India "most favored nation" trading status.
The South Asian neighbors have fought three wars, two of them over the Himalayan territory of Kashmir, since the 1947 partition of the subcontinent into Islamic Pakistan and Hindu-majority, secular India after independence from Britain.
Last year, both nations pledged not to let their fragile peace process unravel again over the range of thorny issues that put them at odds.
In 2004, the nations agreed to negotiations that cover eight issues, including Kashmir, terrorism and Pakistan's concerns over river dams on the Indian side of the border, which it sees as a threat to its water supplies.
Since then, successive governments have held talks in an effort to end the historical acrimony.
Singh and Zardari hailed results from the dialogue in September 2008 as the countries completed four rounds of diplomatic meetings.
But engagements were suspended two months later in November 2008 after the terrorist assault on Mumbai, which left more than 160 people dead.
Over the past two years, India and Pakistan have held a series of high-level meetings in their bid to put their peace dialogue back on track, a process considered crucial to regional stability ahead of the withdrawal of U.S. troops from Afghanistan.
In 2011, New Delhi and Islamabad agreed to resume talks.
"It's a win-win situation when Pakistan and India are engaging in dialogue, are talking to each other, and are building better cooperation," Mark Toner, a deputy spokesperson for the U.S. State Department, said Thursday regarding Zardari's India visit.
Observers say the Sunday lunch meeting between the Indian and Pakistani leaders was encouraging.
"The lunch being hosted by the prime minister for a Pakistani president on a private visit is a welcome step," said Uday Bhaskar, a strategic analyst.