Indian Prime Minister Manmohan Singh, right, shakes hands with Pakistan's President Asif Ali Zardari during a meeting in New Delhi. (HO/PAKISTAN'S PRESS INFORMATION DEPARTMENT/AFP/GETTY IMAGES)

A religious pilgrimage to India by Pakistani President Asif Ali Zardari on Sunday led to talks with Indian Prime Minister Manmohan Singh that both leaders said held the promise of improved relations between the historically hostile nations.

During a private meeting that lasted 40 minutes, Zardari and Singh discussed fighting terrorism and facilitating trade, officials said. The Indian leader also accepted Zardari’s invitation to visit Pakistan, which Singh has not done since becoming prime minister in 2004.

Although accompanied by a delegation that included his interior minister and foreign secretary, Zardari insisted to reporters in New Delhi that he was traveling as a private citizen. Before leaving Pakistan, he also said that he was calling on Singh only as a courtesy while en route to pray at the shrine of a 12-century Sufi saint revered by both Muslims and Hindus.

But Zardari’s visit to India — the first by a Pakistani head of state in seven years — comes at a time when Pakistan’s civilian and elected leaders seem determined to wrest a measure of foreign policy decision-making power from the nation’s military.

As a matter of course, Pakistan’s army and intelligence services paint India as an existential enemy always poised to strike. It is a tactic, critics say, to ensure that the military’s influence and huge budget are not questioned.

India and Pakistan have fought three wars since independence from Britain in 1947 and have failed to resolve differences on the central dispute over the Himalayan region of Muslim-majority Kashmir. Pakistan accuses India of widespread human rights abuses in Kashmir, while New Delhi says Pakistan-based groups foment terrorist attacks in India.

After their meeting, Zardari and Singh called for an overall better relationship between the nuclear-armed neighbors, while not disclosing specifics.

“We have spoken on all the topics that we could have spoken about and are hoping to meet on Pakistani soil very soon,” the Pakistani president said.

“We have a number of issues,” Singh added, “and we are willing to find practical, pragmatic solutions to all these issues.”

In the past year, both nations have been trying to encourage what has come to be known in the Indian capital as “soft diplomacy” — easing trade restrictions, cooperating on cultural exchanges and bonding over cricket, a sport beloved by Pakistanis and Indians.

“Improving relations with Pakistan is the most important foreign policy item left on Manmohan Singh’s agenda in the remainder of his term,” said Sanjaya Baru, a senior fellow at the New Delhi-based Center for Policy Research and a former Singh adviser.

Singh’s term ends in 2014, and Zardari’s ends in 2013.

The two nations, despite their long military standoff, resumed a fragile peace process a year ago, after a two-year diplomatic deadlock triggered by attacks on Mumbai that killed 166 people in 2008 and that India blamed on Pakistani terrorists.

Zardari arrived in the shadow of a U.S. announcement last week of a $10 million bounty for the arrest of Hafiz Mohammad Saeed, founder of Lashkar-i-Taiba, the Islamist group alleged to have planned the attacks.

The United States, the United Nations and India have designated Saeed an international terrorist, but Pakistan says no one has produced conclusive proof of his complicity in the attacks.

India’s foreign secretary, Ranjan Mathai, told reporters that Singh raised the issues of terrorism and Saeed with Zardari.

Zardari, according to Mathai, said the Saeed matter would be discussed between officials of the two countries.

The handshakes and smiles notwithstanding, the practical results of the micro-summit are another matter. In a column beforehand, Indian Express editor Shekhar Gupta noted that Sunday’s meeting was between “two struggling leaders.”

In the past two years, Singh has lost much domestic credibility, with his government blamed for corruption, slowing economic growth and policy paralysis. Zardari, meanwhile, is widely seen by analysts and the public as corrupt and ineffectual.

But if nothing else, Zardari’s pilgrimage to the marble-domed Sufi shrine in Ajmer, a town in the western state of Rajasthan, sent a message against Islamist extremism.

Suicide bombers in Pakistan have repeatedly targeted worshipers at the graves of Sufi saints in a campaign to forward militants’ views that the sites violate Islamic tenets.

On Sunday, Zardari and his son, Bilawal Bhutto, carried floral offerings in baskets wrapped in red-and-green satin fabric over their heads into the tomb. After prayers, they emerged wearing pink and red religious turbans and waved to the cameras. Zardari had visited the shrine in 2005 with wife and former Pakistani prime minister Benazir Bhutto, who was later assassinated.

“It is a bold statement by Pakistan’s President Zardari to come to this shrine at a time when there are fears of hard-liners taking over everywhere,” said Salim Mahajan, an Indian activist for Sufism. “It is a good signal he is sending about the tolerant and assimilative form of Islam.”

Zardari wrote in the shrine’s register that he felt “a great spiritual happiness” after praying there.

Leiby reported from Islamabad, Pakistan.