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NEW DELHI — India’s new prime minister, Narendra Modi, celebrated his 64th birthday on Wednesday by hosting President Xi Jinping of China in his home state of Gujarat, as the leaders of Asia’s two giants lay the foundation for a long-term relationship that carries huge stakes for both.

It is the first visit of a Chinese president to India in eight years — only the third in history — and the reasons for mutual good will are compelling.

China has the ability to channel billions of dollars into Indian infrastructure and manufacturing projects, allowing Modi to pursue the job-creation agenda that was at the heart of his campaign. China, meanwhile, needs calm on its southwestern border to offset tense relationships with Japan, Vietnam, the Philippines and the United States. State-run Chinese newspapers have lavished praise on Modi, intimating that he has the potential to set India on a Chinese-style economic growth trajectory.

But those interests are balanced by deep historical mistrust on security matters.

Indeed, even as India prepared an opulent riverfront dinner for Xi in Gujarat this week, troops and slogan-chanting civilians were facing off along the disputed border between China and India, where the two countries fought a brief war in 1962. India has discussed beefing up maritime cooperation with the navies of Australia and Japan and proposed tighter defense and energy ties with Vietnam — all moves that could be seen as a challenge to China. Meanwhile, China is building ports and other facilities throughout South Asia, a so-called string of pearls strategy that India views warily.

M.J. Akbar, a spokesman for Modi’s Bharatiya Janata Party, said the new government would assert India’s role as a leading power in the region without fear of irritating China.

The Chinese leader’s three-day visit will be marked by a charm offensive on both sides. In what officials described as an unusual gesture, Modi agreed to greet Xi in person Wednesday when he arrived at his hotel in Ahmedabad, the commercial hub of Gujarat. The two were then scheduled to meet at a private dinner.

In a commentary published Wednesday in The Hindu, a daily newspaper, Xi argued for closer economic cooperation between China and India, which he described as “the world’s factory” and the “world’s back office.” He said China could help India improve its infrastructure and manufacturing base and open Chinese markets to Indian pharmaceuticals and IT services — a move that could narrow the $30 billion trade imbalance between the two countries.