MADRAS, India — Maybe the world is breathing easier now. There will probably not be a nuclear conflict between the two long warring Asian rivals, India and Pakistan. There are distinct signs of de-escalation between their armies, which have stood in a defiant eye-to-eye confrontation for several months.

India has just ended a five-month ban on Pakistani aircraft entering its airspace. It also has withdrawn its navy from waters near Pakistan, and has named an ambassador to Islamabad.

Admittedly, a million soldiers on either side of the border keep their fingers on the triggers of their guns, but there is some softening in their stance for the first time since December, when Islamic terrorists from Pakistan attacked India’s Parliament in New Delhi.

These changes have come about thanks to American pressure.

U.S. Defense Secretary Donald Rumsfeld, who visited India and Pakistan some days ago in an attempt to stop what seemed like imminent war, said New Delhi’s latest measures were “very useful.” But he regretted that tension remained uncomfortably high.

Washington has much to lose in the event of full-scale fighting between the two neighbors, who have been quarreling for more than 50 years over Kashmir.

First, American troops are still in Pakistan trying to stamp out al-Qaeda and, more importantly, capture the terrorist organization’s leader, Osama bin Laden, the mastermind behind the Sept. 11 tragedy in New York and Washington, D.C. If hostilities break out, there could be American casualties, something the U.S. public would not tolerate.

Second, Pakistani soldiers now helping the United States flush out bin Laden’s men in Afghanistan and elsewhere would have to be moved to the frontline for the war with India.

The current peace process — encouraged and guided by Washington — is important not just for America but for the rest of the world, which can ill afford to have a nuclear conflagration in South Asia. But if peace is to succeed, it must pass through two phases.

Islamabad must end its support for the radicals whose aim has been to wrest control of Kashmir, a Muslim majority state divided between India and Pakistan. What’s more, Gen. Pervez Musharraf, Pakistan’s president, must go beyond mere rhetoric: He must disband dozens of training camps on his soil that have served as a breeding ground for religious fundamentalists. The camps have for years trained ultras who have crossed over to India to wage, what most major powers now admit, was a proxy war.

New Delhi, meanwhile, should get back to the negotiating table and resume a dialogue on how best to sort out the Kashmir imbroglio.

Both sides understand this, but have their own domestic compulsions that could easily lead to the proverbial slip between the cup and the lip. Rumsfeld’s trip was meant to prevent that slip, but nobody is certain how successful he was.

He ought to have realized that Musharraf has a high stake in keeping alive the Kashmir issue: The general’s army wants it, and the nation’s vengeful zealots will refuse to let Kashmir out of their hands. Musharraf is obviously unwilling to be seen as soft on the Kashmir question unless New Delhi gives significant concessions. Whether it will is not yet clear. Rumsfeld himself probably went back home without the faintest clue.

America often calls India a great democracy, but it has little idea of who really is in charge there. Indian Prime Minister Atal Behari Vajpayee and Foreign Minister Jaswant Singh are moderates, but Defense Minister George Fernandes and Home Minister L.K. Advani are hawks with their own agenda on Kashmir.

In fact, Advani now says that unless Pakistan shuts down the terrorist camps, New Delhi will not talk. There are also indications that India’s armed forces are itching for a fight. If the next terrorist attack is nasty enough, they could get their way.

For the time being, though, Indian moderates appear to be in control. They have acknowledged that cross-border terrorism has eased somewhat, and have begun a “calibrated response.” New Delhi is considering a U.S. offer to electronically monitor the line of control dividing Kashmir.

However, most of the Indian soldiers deployed in Kashmir probably will remain until elections there this autumn. New Delhi hopes to cure Kashmiri separatism at the polls, which it hopes will produce a popular government willing to negotiate a political deal.

Islamabad’s ultimate prize will be a discussion on Kashmir, which is viewed in Pakistan as stolen property. Multireligious India sees no reason to give up a state that acceded to it legally. Talking to Pakistan will change none of that.

The world understands this perfectly well. What the U.S. and others should do is try to get New Delhi to sit across the table and talk on Kashmir, and maybe treat the people there a little more decently than in the past. For Musharraf, desperate as he is to squeeze his way through a formidable obstacle, this by itself might be a big victory.

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