The royal couple greeted the president and his wife Mary at London's Royal Garden Hotel close to their Kensington Palace apartments, two years after they first met the foreign leader during the Diamond Jubilee tour to south east Asia in 2012.
William and Kate later accompanied the visitors to Whitehall to meet the Queen and Duke of Edinburgh.
The royals led the procession back to Buckingham Palace for a reception hosted by the Queen. Although Kate is said to be feeling better, The Mirror reports she didn't join the family for lunch after the carriage procession along the Mall.
The duchess has been forced to cancel previous public appearances due to a severe bout of morning sickness, hyperemesis gravidarum.
She was last seen at a public engagement when she opened a poppy installation at the Tower of London with Prince William and Prince Harry in August - a month before her pregnancy was confirmed on 8 September.
On Monday, more royal baby news was announced. Kensington Palace revealed Kate and William are expecting their new arrival in April 2015.
This news suggests Kate is now 12 weeks pregnant - and there has already been speculation that the royal baby's birth could coincide with the couple's fourth wedding anniversary on 29 April or the Queen's 89th birthday on 21 April.