The formal meeting between Mrs. Obama and Xi, in the company of Xi's wife, Peng Liyuan, and Mrs. Obama's two daughters and mother, took place in a state guesthouse after the first lady toured a Beijing high school and the former Imperial Palace.
"I cherish my sound working relationship and personal friendship I already established with your husband," Xi said. "We stay in close touch between phone conversations and correspondence."
Mrs. Obama thanked Xi for the warm reception for herself and her family. "We have had a wonderful first day here in China," she told Xi.
The meeting was not on the first lady's official itinerary but was expected. "It is only logical for President Xi to meet her, because it is a matter of etiquette for the head of the household to meet the guest of his wife," said Teng Jianqun, director of the American studies department at China Institute of International Studies. He added that Mrs. Obama likely served as a messenger on behalf of President Barack Obama.
Her visit to China is being viewed as a prelude to an upcoming meeting between Xi and President Obama at a nuclear security summit in The Hague, when more thorny issues will be raised.
Mrs. Obama also made history as the first U.S. first lady to visit China independently, Teng said.
The first lady told Xi she was focusing on education and student exchanges during her seven-day, three-city visit to China. Her aides have said the first lady plans to stay away from contentious issues.
Earlier on Friday, Mrs. Obama visited with excited students who were building robots and tried her hand at Chinese calligraphy at the Second High School Attached to Beijing Normal University in central Beijing. The elite school has 33 American exchange students, and some of its Chinese students aspire to study in the United States.
In a calligraphy class set up for Mrs. Obama's visit, the first lady practiced writing the Chinese character for "eternal" under the guidance of 16-year-old student Lu Yuhong.
"I'm nervous," Mrs. Obama said. "Don't be nervous," Peng replied in English.
Lu said he too was nervous, as well as "very excited."
"But the first lady was so amicable. She was very approachable," Lu said.
Peng also picked up a brush and wrote a four-character Chinese aphorism on virtues before presenting it to Mrs. Obama as a gift.
In another class, students showed the first lady small robots they had built, moving the devices with remote controls. One knee-high robot climbed over a pile of yellow plastic bricks.
"All the students that she met with, the Chinese students, spoke English and were able to explain to her in very fluent English what they were doing," said Tina Tchen, Mrs. Obama's chief of staff. "And I think she found that very impressive, because we know it's something that we struggle with in the United States, about having our kids be able to be fluent in a second language by the time they get to high school."
Lu, the student, said he had bonded with American friends over a shared love of U.S. television, including his favorite series, "Agents of S.H.I.E.L.D."
Among the six American exchange students attending the calligraphy class was Audrey Fritz, 17, at the exclusive Sidwell Friends School in Washington.
"It's been an amazing experience," Fritz said of her time in China. "I have learned to be much more independent."
Later in the morning, Peng went with Mrs. Obama to the former Imperial Palace in central Beijing. That was to be followed by a private dinner and a performance. On Saturday, the first lady was due to speak at Peking University and on Sunday visit the Great Wall.
At Peking University, Mrs. Obama plans to speak on the importance of free exchange of ideas, her aides said.
"I do think tomorrow she will talk about the value of the free exchange of ideas and the Internet, and how that, in her view, has made our country stronger; how even when you can be the object of criticism, as she and her husband have been, that that's not a system that she would change," Tchen said.
White House aides have said they hope Mrs. Obama traveling with her daughters and mother can resonate with Chinese families who value multigenerational activities.
"China views Mrs. Obama's trip most positively," said Shen Dingli, professor of international relations at Fudan University in Shanghai. "If she is humble and respectful, she will win the support from the Chinese public for building good relationships with the United States under the leadership of her husband."
The Obama delegation is due to fly Monday to Xi'an, home to the famed Terra Cotta Warriors Museum, then visit a panda breeding facility outside Chengdu in the southwest.
This is the first lady's first trip to China.