With wary eye on the U.S., China courts India NEW DELHI (Reuters) - Chinese Premier Li Keqiang, smiling and effusive, was out to smooth ruffled feathers in India this week, promising to ease tensions and increase trade between Asia's fastest growing economies in his first trip overseas since taking office. "China will make your dream come true," Li told a banquet hall filled with Chinese and Indian business executives in the financial capital of Mumbai as he wound up his visit on Tuesday. China's overtures, which come amid worries in Beijing that it is being encircled by the United States and its allies, however met with a cool response. India has been shaken by a recent border spat with China and is cautious about Beijing's friendship with rival Pakistan, where Li flies on Wednesday. New Delhi is also concerned about a ballooning trade deficit with China and a flood of cheap Chinese-made goods undercutting local manufacturers. While India's relations with the United States are cordial and it is a major purchaser of its weapons, New Delhi has stayed away from a close strategic alliance. "We would not like to see India become a tool of other major countries, especially the U.S., to counterbalance or check or contain China," said Hu Shisheng, an India specialist at CICIR, a Chinese government-backed think tank in Beijing. We want, through closer relations, to support New Delhi's policy that maintains equal distance. It's not realistic to expect India to be closer to one country than the other. Li, who is travelling with executives from 41 Chinese companies, said the two rapidly-growing economies should free up bilateral trade and do more business together, instead of relying on others for development. "With a long border and extensive common interests, China and India should not seek cooperation from afar while neglecting the partner close by," he said in a speech to businessmen and diplomats earlier on Tuesday. Chatty and relaxed, Li repeatedly took Prime Minister Manmohan Singh by the hand and said a visit to India 27 years ago influenced him much as exposure to the sub-continent had affected Steve Jobs, the legendary co-founder of Apple. Singh smiled back, but hardened India's stance on the long-standing territorial dispute between the two nations, saying broader ties could not blossom without peace on the border. In the past, India has sought to separate the border dispute from wider relations. The difference this time was that Li's visit came just weeks after Chinese troops set up camp 19 km (12 miles) inside territory India claims as its own. The stand-off, which only ended on May 3 after three weeks of high-level negotiations, caused a public outcry in India. It overshadowed preparations for Li's trip and may explain the lack of significant bilateral agreements signed. Despite the large commercial delegation, only one major business pact was signed, a $1 billion debt-for-fuel deal between China and Essar Energy PLC Lt, part of India's Essar group. Smaller pacts added a total $500 million in deals. China and India disagree about large areas of their 4,000 km (2,500 mile) border and fought a brief war 50 years ago. There has not been a shooting incident in decades but the feud prevents normal trade relations between neighbors, who account for 40 percent of the world's population. Lalit Mansingh, a former Indian foreign secretary, the top official in the external affairs ministry, said he detected a new openness between the leaders of the two countries, and a willingness to tackle thorny issues. But he said the recent border confrontation had severely tested India's patience. They don't want us to get closer to the Americans. But ironically, that is exactly what they are doing by being extremely provocative at the border," Mansingh told Reuters, adding that China was also irking neighbors with maritime disputes with Japan and nations in Southeast Asia. By picking up a fight with every single neighbor after a period of friendship with all neighbors, the Chinese are, in fact, getting people together in a line up against them. On the back of this week's visit, both Prime Minister Singh and Premier Li are due to visit each others respective rivals. Next week, Singh is headed to Japan, which is engaged in an increasingly edgy dispute with China over a group of islets in the seas between them. Li goes to Pakistan, where he is to sign agreements to develop the Chinese-managed Gwadar port. India has often been nervous about Chinese agreements with its neighbors that are not strictly military but could be leveraged in a conflict. Indians sometimes refer to these as a "string of pearls," which include China's ties with Pakistan, access to a Myanmar naval base, Chinese construction of a deepwater port in Hambantota, Sri Lanka, and its deepening ties with Nepal and the Maldives. Its force deployments in Tibet add to India's stress. In Beijing, there are worries that the country is being encircled by the U.S. strategic pivot to Asia and its allies like Japan, South Korea, Taiwan, the Philippines and more recently, Vietnam. China has also been closely watching the improvement of U.S. ties with Myanmar and India. After the border, India's biggest gripe with China is over trade. From almost nothing in the 1990s, bilateral trade hit a peak of $73 billion in 2011, heavily skewed in China's favor. In comparison, China's annual trade with Japan is close to $300 billion. On Tuesday, Li pitched hard for closer economic cooperation and said Chinese companies could help India rapidly modernize its skeletal infrastructure. "Our industrial structures are highly complementary, India has a competitive edge in IT, software and bio-medicine, while China is seeing rapid expansion of its machinery, textiles and emerging industries," Li said, and offered talks on a free trade agreement. But India complains that China does not give its pharmaceutical and IT companies fair market access. One Indian trade official, speaking to Reuters, burst out laughing at the free trade proposal, saying there was no way India would consider it until the trade imbalance was addressed. That may take some time. In a joint statement signed on Monday, China reiterated it would increase access for Indian products. The same was said on a visit by Premier Wen Jiabao in 2010 - but last financial year, India's bilateral trade deficit grew to $41 billion. Additional reporting by Annie Banerji, Satarupa Bhattacharjya and Devidutta Tripathy in NEW DELHI; Henry Foy in MUMBAI and Terril Jones in BEIJING; Editing by Raju Gopalakrishnan