For the past two days, Delhi's wide, tree-lined boulevards have suffered worse traffic jams than usual. The cause has been innumerable "VIP movements", as journeys undertaken by those considered important enough for all other traffic to be held up, sometimes for hours, are described in South Asian bureaucratic speak.

The most momentous "VIP movements" of the week were those of Narendra Modi to and from his inauguration as 15th prime minister of the world's biggest democracy on Monday night. But the intriguing possibility of another sort of trip was raised – one which might be the most ambitious yet in the astonishing career of a man who has risen from tea seller to leader of 1.25 billion people.

The trip in question would be to Pakistan, the hostile neighbouring state with which India has fought three wars and one smaller conflict. Such a visit – if successful - could unlock a whole cascade of hugely beneficial consequences for both nations, for the region and beyond.

A few months ago, the probability of Modi, a Hindu nationalist, playing peacemaker to a Muslim state such as Pakistan seemed slim.

However Modi surprised observers last week by inviting Nawaz Sharif, the prime minister of Pakistan, to his inauguration ceremony.

The invitation from Modi, reviled in much of the Islamic world as a sectarian bigot, posed a dilemma for Sharif, who leads the conservative Pakistan Muslim League. But, despite vocal domestic opposition, he flew to Delhi, caused more road closures and became the first Pakistani premier to attend the inauguration of his Indian counterpart.

A 50-minute meeting might have produced little of substance – Modi reiterated India's longstanding complaints about terrorists launched from Pakistani soil to wreak havoc on its interests and citizens, Sharif uttered platitudes about an "historic opportunity" – but even the banality of the diplomatic boilerplate could not hide an unexpected sense of optimism.

The invitation to Modi to visit Pakistan – though in part a diplomatic nicety – boosted spirits further.

Modi's predecessor, Manmohan Singh, had been keen to travel to Pakistan during his decade in power but was stopped by his centre-left Congress party. Modi's potent nationalist credentials and the landslide victory of his Bharatiya Janata party (BJP) open other possibilities.

"Modi doesn't have to watch his back like Manmohan Singh and so could theoretically say OK. If there is some momentum generated and the two sides resume serious talks then it is just about possible to imagine a visit," said Manoj Joshi, a Delhi-based commentator.

This is not the first time there has been hope, albeit slim, of some kind of breakthrough.

Sharif said the two nuclear-armed nations could "pick up the threads" of a previous visit to Pakistan by a BJP prime minister, Atal Bihari Vajpayee, in February 1999.

Though that visit resulted in a treaty greeted warmly on both sides of the border, it did not however prevent a short war launched by the Pakistan military months later which froze relations once more.

Vajpayee did visit Pakistan again in 2004, when a regional summit gave new momentum to peace efforts. These lasted until Pakistan-based militants launched a spectacular and bloody attack on Mumbai, the Indian commercial capital in 2008.

But Sharif and Modi both have strong mandates and appear convinced better relations can and should be built through trade whatever other considerations there may be. Commerce between Pakistan and India remains at negligible levels and the flagging economies of both countries badly need a boost.

Among the manifold obstacles to warmer ties, the greatest is mutual suspicion. If Indians blame terrorism in their country on Pakistan, many Pakistanis - including some in the most senior ranks of the powerful army - are convinced India is fomenting violence in theirs. Both states manoeuvre for influence in fractious, fragile Afghanistan. Kashmir is a visceral issue for hard-liners.

Serious progress in the immediate future still looks improbable. But if the VIP movements of the past two days lead to more ambitious international ones, the drivers of Delhi may see them as worth the wait.