Over kung pao chicken and dumplings, Pentagon chief Chuck Hagel recalled his days as an infantryman in Vietnam Wednesday with young Chinese soldiers at a People's Liberation Army (PLA) training academy.

"Many, many years ago when dinosaurs roamed the earth, I was a sergeant in the army," joked the visiting US defense secretary before sitting down to lunch at a canteen with soldiers training to become non-commissioned officers (NCOs) in the PLA.

The Changping school laid out the red carpet for Hagel, who did his NCO training in 1968 after braving combat in the jungles of the Mekong Delta -- and still carries shrapnel in his chest as a result.

The atmosphere was friendly and conversation light, in stark contrast to the rough reception Hagel received Tuesday from top Chinese officials and a roomful of PLA colonels who peppered him with tough questions.

Then, a whole range of disagreements were on display, with critical editorials in Chinese media and a testy exchange with General Fan Changlong, vice chairman of China's Central Military Committee, officials said.

The general told Hagel that China was "dissatisfied" with his remarks about Beijing's territorial disputes with Japan and other countries, state news agency Xinhua reported.

Hagel strongly disagreed and "pushed back", US officials said.

But at the NCO training academy in a northwestern suburb of Beijing, Hagel faced no grilling over US foreign policy, and instead watched soldiers in combat fatigues drive bulldozers and backhoes in a precision display.

At the canteen Hagel picked up a tray of kung pao chicken, broccoli and dumplings before lunching with two Chinese cadets and asking them about their careers in the army.

Non-commissioned officers were a crucial foundation for any military, he told them.

"This is a very important institution. You're the leaders of the next generation so we need the best people."

The training school is located near the Badaling section of the Great Wall, visited by US president Richard Nixon during a groundbreaking 1972 trip that set US-China relations on a new course.

China has since become an economic giant with an increasingly powerful military, and Washington is struggling to manage its rivalry with Beijing without inciting tensions or crises.

Throughout his visit to China, which included a tour of the country's first aircraft carrier, Hagel has stressed the importance of an open and pragmatic dialogue between the two armed forces, saying disagreements should be confronted "straight up".

Speaking at the PLA's National Defence University on Tuesday, Hagel pleaded for restraint on territorial claims and more contact between the top brass, saying the more the countries' commanders speak to each other, the less chance of a mistake or a "miscalculation".

"We must all find ways to get along... it's just too important for each of us and the rest of the world," he said.

After the training school, Hagel wrapped up his three-day tour by meeting President Xi Jinping, and officials said the discussions went more smoothly than Tuesday's "frank" exchanges.

The two discussed the importance of expanding US-China military relations as well as North Korea's nuclear programme, a Pentagon spokesman said.

Hagel stressed the need to "achieve a complete, verifiable, irreversible denuclearisation on the Korean peninsula in the face of the growing threat posed by North Korean nuclear and missile developments", said Brent Colburn, assistant to the defence secretary.

Washington has appealed to Beijing to rein in the North Korean regime, and China's "tone" in this week's discussions was more positive than in previous talks, said a US administration official, who spoke on condition of anonymity.