NEW DELHI — The leaders of India and China papered over their recent border spat on Monday with a friendly joint statement and an array of promises for economic and military cooperation, but they resolved none of their most vexing problems. 

The Indian prime minister, Manmohan Singh, emphasized in his remarks that cordial relations between the countries depended on “peace and tranquillity on our borders,” and said he and his Chinese counterpart, Li Keqiang, had “agreed that this must continue to be preserved.” 

Mr. Li, who arrived in India on Sunday, offered some reassurances about the border difficulties, but he made no apology for Chinese troops’ recent incursion into a district of Kashmir claimed by India. 

“Both sides believe we need to improve various border-related mechanisms that we have put into place and make them more efficient, and we need to appropriately manage and resolve our differences,” Mr. Li said.