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Michelle Obama greeted warmly by China’s leader

On the first day of her weeklong visit to China on Friday, Michelle Obama played table tennis at the Beijing Normal School in Beijing.Any Wong/Associated Press/Pool

BEIJING — Michelle Obama met with President Xi Jinping on Friday, the first day of her weeklong visit to China, in a sign that the leaders of the world’s two largest economies are seeking to build stronger bonds.

The formal meeting between Obama and Xi, in the company of Xi’s wife, Peng Liyuan, and 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.’’

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.

Later in the morning, Peng went with Obama to the former Imperial Palace in Beijing. That was to be followed by a private dinner and a performance. On Saturday, Obama is to speak at Peking University .