US First Lady Michelle Obama took her daughters and mother to Beijing's former imperial palace Friday, on a China tour the White House emphasises will be light on politics and heavy on personal diplomacy.

Obama, her daughters Malia and Sasha, and her mother Marian Robinson along with China's own first lady Peng Liyuan took a guided tour of the sprawling Forbidden City, waving to onlookers outside the central pavilion known as the Hall of Supreme Harmony.

The two women's husbands, Barack Obama and Xi Jinping, are expected to meet next week on the sidelines of a nuclear security summit in the Netherlands.

Xi later welcomed the first lady at the Diaoyutai State Guesthouse.

"I cherish my sound working relationship and personal friendship I have already established with your husband, and we stay in close touch through meetings, phone conversations and correspondence," he said.

"I wish to thank the US side for sending such a heavyweight ambassador to China," he added.

Obama said she was going to focus her visit on education, "which is an important issue to both of our countries".

The visit is Obama's first to China, and her third foreign trip without the US commander-in-chief since moving into the White House.

Beijing and Washington have hailed the week-long tour as an opportunity for both first ladies to highlight the importance of education and "people-to-people" exchange.

- Peng's 'delight' -

But critics in the US have lambasted signals that human rights are off the agenda -- although Obama is scheduled to eat at a Tibetan restaurant in Chengdu -- and the cost to taxpayers, which the White House has declined to reveal.

Obama, her family and Peng began the day with an hour-long visit to the No. 2 High School Attached to Beijing Normal University, where they observed students learning how to build robots, visited a calligraphy class and dropped in on a group of pupils playing ping-pong.

The two first ladies smiled broadly and shook hands on a red carpet in front of the school -- their first ever meeting -- as students around them waved flags.

Obama told Peng that it was "truly an honour and a privilege" to visit China with her family.

"It's very rare that I have the opportunity to travel outside of the United States, and it's even more rare to have the opportunity to travel with three generations -- with my daughters, and with my mother," Obama said.

Peng said it was "a great delight" to meet her, saying: "In China, we have an ancient idiom, which means when two people meet for the first time, they may feel as if they have known each other for many years."

At the school's Geometry Robotics Lab, students demonstrated their machines for the first ladies and Obama tried her hand at operating one by remote control.

Obama exchanged a few table tennis strokes with a young woman, and told the crowd she was a novice. "My husband plays," she added. "He thinks he's better than he really is."

At a calligraphy demonstration a 16-year-old student taught Obama how to draw the Chinese character for "eternity", before the visitors looked on as Peng adeptly wrote out a four-character aphorism meaning "Great virtue promotes growth".

She signed her name and presented the calligraphy to Obama as a souvenir.

Later, at the Forbidden City, they saw a number of sites not open to the general public, including the Hall of Earthly Tranquility, which used to house the emperor's concubines.

- 'China 1 US 0' -

The trip has been front-page news in China's state-run media, and several outlets have run op-eds hailing the planned focus on "soft" issues such as education rather than on political topics.

"When briefing the media about Michelle's trip, the US side said the first lady is to steer clear of politics, human rights, trade disputes and other bilateral differences -- issues better handled via official diplomacy," the official Xinhua news agency wrote in a commentary Thursday.

"That approach is right. The uniqueness of the role of first ladies is its soft touch and freedom from the knottiness and even ugliness of hard politics."

Both women's fashion choices were a hot topic on Sina Weibo, a Chinese equivalent of Twitter, with some Chinese Internet users favourably comparing Peng's formal attire -- a navy blue jacket and skirt -- to Obama's more casual black trousers, vest and white silk shirt.

"Michelle's clothing is too old-fashioned," wrote one Weibo user. "China 1, US 0."

The question of the trip's cost has drawn attention on both sides of the Pacific.

Chinese social network users widely circulated a China National Radio report on the lavish 52,000-yuan-a-night ($8,400) hotel suite where it said the Obama family were staying.

According to the hotel website, the suite is 320 square metres (3440 square feet) and includes a kitchen, bar, sauna, jacuzzi, dining table for six and a treadmill.