The two nuclear-armed neighbors have been perilously close to all-out war since the end of 2001, when five terrorists were killed trying to seize New Delhi’s Parliament building. India blamed separatist guerrillas supported by Pakistan in the disputed territory of Kashmir. Both countries withdrew their ambassadors and traded tit-for-tat ballistic-missile tests, as well as artillery fire and mortar barrages.

This April, Vajpayee visited the Kashmiri city of Srinagar, where he made the first public speech there by an Indian prime minister since Rajiv Gandhi’s. Vajpayee, in his 17-minute address, expressed openness to new talks with Islamabad. Pakistan’s prime minister, Zafarullah Jamali, telephoned Vajpayee early last week and invited him for a visit. Places and dates for top-level talks are still under discussion, but senior diplomats from the two countries are expected to begin meeting as early as this week.