After touring the Emirates Arena, one of the venues for the 2014 Commonwealth Games, William and Kate greeted onlookers who had gathered outside.
Four-year-old Shona Ritchie asked William if he would give her a kiss.
He agreed and as he leant in to kiss her cheek the girl pulled away, causing laughter from those around, including the British prince.
Nearby, his wife Kate, the Duchess of Cambridge, who is five months pregnant, refused to comment on potential names for their child.
"No, no names. We don't know what it is," she said.
One woman who waited outside the arena to greet the royals told British broadcaster Sky News that she asked William to kiss her young daughter.
"Prince William came across and had a little chat with us. We asked if he wanted to give Heidi a kiss, but apparently he'd already been refused a kiss from someone else," she said.
Later in the day the royal couple, who are called the Earl and Countess of Strathearn when in Scotland, visited a homeless shelter run by the Quarriers charity, where William turned his hand to disc-jockeying.
William's father, Prince Charles, is due to join the couple on Friday, when they will visit a stately home, Dumfries House, in Ayrshire.