Michelle Obama brought the importance of education to the fore on Sunday on the third day of a visit to China, where she has won praise for her approachability and admiration for her comments supporting freedom of speech.

Her comments were made on Saturday, the day the New York Times and Der Spiegel published reports, based on documents leaked by Edward Snowden, that said the US National Security Agency had inserted “back doors” into networks maintained by the Chinese telecoms giant Huawei. On Sunday her husband, President Barack Obama, was due to leave for a visit to Europe which will include a Monday meeting with the president of China, Xi Jinping.

Obama, travelling with her two daughters, has been photographed at famous spots including the Forbidden City and Great Wall during the first independent trip by a US president's wife to China. She has won compliments for her elegant clothing and her interactions with ordinary people in a country where it is rare to see leaders' spouses or children in public.

"She is very warm and frank, and when she is talking to people she conscientiously listens to what they have to say," said Wu Qing, a retired professor of Beijing Foreign Studies University who met Obama on Sunday.

"In China, we usually use weather to express our mood or state of mind, so the fact that the weather has been so nice these few days means she is very welcome in China.”

Obama hosted a discussion about education with a handful of Chinese professors, students and parents, as well as the new US ambassador to China, Max Baucus, at the US embassy on Sunday morning. In the afternoon, she visited part of the Great Wall in the northern Beijing suburbs with her daughters, 15-year-old Malia and 12-year-old Sasha, and her mother, Marian Robinson.

There, the first lady and her daughters walked a stretch of the wall that looks out to a massive rock inscription on a hillside that reads in Chinese: "Loyal to Chairman Mao."

T-shirts of President Barack Obama in a Mao hat that are common at Beijing tourist sites were absent from souvenir stalls Sunday, although at least one vendor showed a whole box of them when asked.

The purpose of Obama's weeklong visit is to promote educational exchanges between the US and China, although she brought up a contentious issue on Saturday in a 15-minute speech at a university. She said that freedom of speech and unfettered access to information make countries stronger and should be universal rights. But she did not criticise Beijing directly in her speech at Peking University's Stanford Centre.

China has some of the world's tightest restrictions on the internet, and Mrs Obama's comments were absent on Sunday from state media but circulated in social media, where they were widely praised.

"I was very impressed by her speech mentioning freedom of speech," said Zhang Lifan, an independent historian who said he had read about it in overseas Chinese media. "Although the Chinese constitution guarantees freedom of speech, Chinese citizens don't really enjoy that right. I think she just reminded China in a polite and mild way that not allowing freedom of speech is not conducive to China."

On Sunday, Obama returned to the safer territory of education. "It's personal, because I wouldn't be where I am today without my parents investing and pushing me to get a good education," she said.

"My parents were not educated themselves, but one of the things they understood was that my brother and I needed that foundation," she said at the embassy before hosting a discussion among professors, students and parents chosen by the embassy. The session was closed to the media.

During the private discussion, Obama asked about China's college entrance exam and how easy it was for graduates to find work, and expressed hopes that society would pay more attention to the disabled and that more students from ethnic minorities would participate in exchanges between the two countries, according to a student at the meeting who would only give her surname, Sun.

Obama toured an elite Beijing high school on Friday in the company of the Chinese president Xi Jinping's wife, Peng Liyuan. On Tuesday, she will visit a high school in the south-western city of Chengdu.

Students who met Obama praised her affability. "She was so approachable," said Lu Yuhong, 16, who guided the first lady in writing the Chinese character "eternal" in calligraphy at the Beijing school. Mu Rongduomijia, 16, said she travelled on Saturday from the north-eastern city of Dalian to Beijing, hoping to hear Mrs Obama's speech. Instead, she waited outside for glimpses of the first lady's entourage.

"It was touching to see so many people waiting for her arrival and departure, and that's because of her personal charisma," Mu said, noting she was impressed with the manners of Malia and Sasha.