US Secretary of State Hillary Clinton on Tuesday closed a tour of rising powers India and China during which she turned to quiet diplomacy to make small but clear advances over key rifts.

Clinton's week-long trip was dominated by a crisis in China over dissident Chen Guangcheng, who took refuge in the US embassy in Beijing, and ended in India where usually friendly US ties have been tested by disagreement on Iran.

In both Beijing and New Delhi, Clinton was circumspect in her public comments, fearing that more robust pressure would backfire. But in cautious statements, India and China both appeared to move forward on US concerns.

Foreign Minister S.M. Krishna, speaking on Tuesday after talks with Clinton, said India has cut back on purchases of Iranian oil and shared the US goal of preventing the Islamic republic from developing a nuclear bomb.

Krishna argued that oil companies were leading the decision on reductions, sidestepping India's past denunciations of a US law that will impose sanctions on countries that continue to buy Iranian oil.

"There is no doubt that India and the United States are after the same goal," Clinton told a news conference before flying back to Washington.

The United States and India have been developing warmer relations since the Cold War. Clinton, speaking Monday in Kolkata, said "two great countries cannot possibly agree on everything" and that the key was to keep dialogue open.

"We will discuss and air every single issue. And I think that's the way you should develop a relationship. So I'm very confident about the relationship going forward," she said.

Clinton travelled to New Delhi to prepare for the US-India Strategic Dialogue, held each year since 2010, which will take place next month in Washington.

In Beijing, Clinton and Treasury Secretary Timothy Geithner took part in the Strategic and Economic Dialogue with China.

While such formal meetings produce few dramatic breakthroughs, US officials are convinced that the exchanges have allowed progress by giving a way for all issues to be discussed with Washington.

US officials said privately that they could not have envisioned reaching a solution with China over Chen without forging relations with Chinese leaders through the annual dialogue and other such settings.

Chen, one of China's best-known activists who was blinded by an illness in his infancy, riled authorities by exposing forced abortions and sterilisations under the one-child policy.

He had spent four years in jail before going under house arrest, where he said he and his family suffered severe beatings.

Days ahead of Clinton's visit, Chen managed to flee to the US embassy. US officials negotiated a deal under which Chen would study at a US university and Chinese authorities would promise his safety.

Reaching the Chen deal in the midst of top-level talks "showed how much the relationship between the two countries has changed so we can have these kind of conversations," a senior US official said after the initial negotiations.

But some US lawmakers and activists voiced concern over the deal, questioning why the US would take China at its word over Chen's safety and accusing President Barack Obama's administration of caring more about relations with Beijing.

While China's official media have criticised Chen and the United States, Chen said Tuesday that authorities were moving ahead with giving him a passport.

The US relationship with India is much friendlier than that with China. But US officials were eager to broaden dialogue, with Clinton meeting Monday in Kolkata with influential regional leader Mamata Banerjee.

Banerjee, who has little background in diplomacy, last year won West Bengal's top job of chief minister as she swept out communists who ruled India's fourth most populous state for nearly 35 years.

In the middle of her trip, Clinton also paid her first visit as secretary of state to Bangladesh, hoping to encourage pro-US sentiment in the moderately inclined Muslim-majority nation.