NEW DELHI — When the prime ministers of India and Pakistan met recently on the sidelines of a regional summit meeting in Egypt, they hammered out a joint statement that seemed to point toward greater cooperation between the nuclear-armed neighbors.

After months of tension over the attacks in Mumbai last November, in which gunmen from Pakistan rampaged through India’s financial capital and killed more than 160 people, the two sides seemed open to the possibility of resuming full-blown talks.

Instead, the mere suggestion of a thaw in relations has been met with fierce public and political resistance in India, providing a nagging reminder of the enormous internal obstacles that both countries face in overcoming their decades-old rivalry.