U.S. Secretary of Defense Leon Panetta delivers a speech on Indo-U.S. Defense Relations at the Institute for Defense Studies and Analysis in New Delhi on June 6, 2012. (Jim Watson/AP)

The upcoming withdrawal of NATO-led troops from Afghanistan and the rising power of China loomed large in talks Wednesday between Defense Secretary Leon E. Panetta and top Indian officials.

During a two-day stop here, Panetta urged Indian officials to take a “more active role” in Afghanistan and tried to allay their concerns about a new U.S. strategy for Asia that aims in part to counterbalance China’s increasing influence and military power.

The overture for increased cooperation comes at a critical time. After several years of ramped-up military cooperation and U.S. defense sales to India, there is a perception among some experts on both sides that the relationship has plateaued.

India is in many ways a linchpin for U.S. interests in the region, with its influence on volatile countries to its west and its shared concerns about China to its east, something Panetta highlighted in a speech in New Delhi on Wednesday.

“We have built a strong foundation,” he said. “But for this relationship to truly provide security for this region and for the world, we will need to deepen our defense and security cooperation.”

In Afghanistan, the United States until recently has encouraged limited Indian engagement, consisting largely of economic development, for fear of spooking India’s longtime rival Pakistan. But with the U.S.-Pakistan relationship at an all-time low, the United States appears to be pushing for deeper Indian engagement that includes training Afghan security forces on a larger scale.

“Over the last 10 years, for a variety of reasons, India has not played a particularly active role in Afghanistan,” said a senior U.S. defense official, who was not authorized to speak publicly.

“It makes perfect sense for the U.S. to want the Indian police to train their Afghan counterparts, said Sadanand Dhume, an India analyst at the American Enterprise Institute. “Let’s face it, Afghan policing standards aren’t about to match Danish ones anytime soon. Indian cops can give Afghan cops something achievable to aspire toward.”

But U.S. officials encountered sharp questions from India about the impending withdrawal of NATO-led combat troops from Afghanistan by the end of 2014.

“The last thing India’s leaders want is to be left carrying the can while the U.S. and its allies rush for the exits,” Dhume said.

Although Panetta has spent much of his eight-day swing through Asia explaining the new U.S. policy on Asia, he was careful in his speech Wednesday to avoid framing it as targeting China.

“The United States welcomes the rise of a strong, prosperous and a successful China,” he said.

India has shown increasing concern about China, especially in light of border disputes between the two nations. In meetings Tuesday and Wednesday, Indian officials appeared to welcome an expanded U.S. presence in Asia, but they also have stressed that containing China is not among their goals.

“They have no interest in picking a fight with the Asian mainland’s other ascendant powerhouse,” said Karl F. Inderfurth, a former assistant secretary of state for South Asian affairs and now at the Washington-based Center for Strategic and International Studies.

India and other Asian countries also have questioned whether the United States’ new China pivot is merely rhetoric, given the severe spending cuts the United States faces in coming years.

Early in the past decade, the budding U.S.-India partnership seemed to promise a boom for the U.S. defense industry. India conducts more military exercises with the United States than any other country, roughly 50 a year.

But in recent years, defense cooperation and sales have hit snags — the largest last year when U.S. firms lost out on a $10 billion Indian fighter jet contract.

Defense deals also have been limited by strict U.S. rules on arms sales, Panetta acknowledged Wednesday.

“We need to cut through the bureaucratic red tape on both sides,” he said, announcing a new effort led by Deputy Defense Secretary Ashton B. Carter to streamline the bureaucratic process for defense sales to India.

“They are getting down to the nitty-gritty work of understanding each other’s bureaucratic structures and political cultures,” Inderfurth said. “This phase of the relationship will have its fits and starts and may at times be frustrating for both sides.”