Kaitlyn Easson was last seen about 5:45pm on Sunday in Galashiels at the Interchange in the town centre.
Police said there was a possible further sighting of her walking alone in Melrose Road about ten minutes later, close to the Queen Centre sports facility, heading in the direction of her home.
Police Commander, Chief Superintendent Catriona Paton, said with Kaitlyn reported missing for almost 24 hours, officers were growing “increasingly concerned” for her welfare.
At a press conference held at Galashiels police station on Monday, Ms Paton said: “As you can imagine, her family are facing the most distressing of times and are longing to know that Kaitlyn has been traced safe and well.
“While I have an extensive number of resources and specialists working tirelessly to trace and find Kaitlyn safely, I am urging and appealing to the public to help us in that regard.”
Asked if police suspect foul play at this point in their investigation, Ms Paton replied: “I have no information at this time to suggest that Kaitlyn has come to any specific harm, so we are continuing to keep an open mind, and continuing to do all we can to trace her safe and well.”
Specialist divers were searching for the young girl on Monday. Police said the Scottish Fire and Rescue Service, Border Search and Rescue Unit, volunteers and specialist teams from Police Scotland, including investigators and air support, were involved in the bid to find Kaitlyn.
Ms Paton said the search party was “a huge operation”.
Kaitlyn has been described as being about 4ft 11in tall, slim with long, brown hair. When last seen, she was wearing a white jumper, brown trousers and boots.
The public have been asked to contact police with any information or footage that they have which could help with their investigation.
A portal has also been set up to provide any details, which could be of help to officers involved in the search.
Police said a significant number of inquiries have been carried out since she was reported missing to police at 8:15pm on Sunday night.