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The royals welcomed the Obamas at the entrance way of Kensington Palace on a rainy day in London.
"We have the same weather in Chicago," the First Lady replied of her hometown.
As the doors swung open, and the group headed inside, they glimpsed young Prince George standing near the foyer. He appeared smartly attired for bedtime in a light-colored robe and pajama pants. Before the Obamas arrived, George had been playing in the drawing room with a stuffed animal dog, which was previously given to him by the Obamas and looks remarkably like Bo, their dog.
The rocking horse behind William was a gift the Obamas gave to Prince George when he was born.
Princess Charlotte was already asleep by the time the Obamas arrived.
Prince William could be heard apologizing for the weather to President and Mrs. Obama.
The Duchess of Cambridge donned a dress by LK Bennett for the affair. The First Lady shook hands with the Duke and Duchess of Cambridge upon greeting but was greeted by Prince Harry with a kiss on both cheeks.
The first lady has been actively involved in Prince Harry's Invictus Games to support wounded veterans. She met with the prince in Washington, D.C., last October and will attend the Invictus Games next month in Orlando.
The Obamas were then welcomed into the Cambridges' Apartment 1A at Kensington Palace. The apartment was formerly the home of Princess Margaret, Queen Elizabeth's sister. William and Harry have turned the Kensington Palace apartment of their mother, the late Princess Diana, into their offices.
Earlier in the day, the Obamas traveled to Windsor Castle for lunch with Queen Elizabeth II and Prince Philip. The queen and prince greeted the president and first lady as their helicopter touched down at the castle.
Prince Philip, 94, drove the president and first lady the short distance to Windsor Castle in his blue Range Rover, a departure from the first family's usual Secret Service escort.
The first lady was dressed for lunch in a purple Oscar de la Renta dress and the queen in pale blue. The four then climbed into a car, with Prince Philip in the driver's seat, and drove together to the castle. Once inside, the four posed for photos before the press.
President Obama, who is staying at Winchester House, also met with Prime Minister David Cameron while in London. The president paid tribute to Queen Elizabeth, who turned 90 on Thursday, while at Downing Street.
"As for her majesty, the queen has been an inspiration for me, like so many people around the world," Obama said. "She is truly one of my favorite people and may we be fortunate enough to reach 90, may we be as vibrant as she is."
The president continued, saying, "She's an astonishing person and a real jewel to the world not just the United Kingdom."
Speaking of the "special" relationship between the U.K. and the U.S., President Obama said, "When the U.S. and U.K. stand together we make the world safer and better."
The Obamas have forged a close relationship with the royal family and have hosted Prince William and Prince Harry at the White House in the past.
The president is visiting Britain after talks in Saudi Arabia with Persian Gulf allies. The royal family on Thursday celebrated the 90th birthday of Queen Elizabeth with public events and a private dinner for close family and friends at Windsor Castle.
ABC News' Arlette Saenz and Katie Kindelan contributed to this report.