Nineteen-year-old Leah Croucher disappeared two months ago in Milton Keynes, on her walk to work.
She was last seen on Buzzacott Lane in Furzton, just after 8.15am on Friday February 15.
On Monday, Thames Valley Police revealed that three new witnesses have reported sightings of a woman of a similar description between 9.30am and 11.15am on the same day.
The witnesses were walking by Furzton Lake, close to where Miss Croucher was last seen.
Two of the witnesses were walking together and described a young woman who was “visibly angry, upset and crying”.
They said she was white, aged approximately 20, around 5ft 4ins tall, with dark brown, shoulder length hair.
The witnesses saw her again 20 minutes later, when they said she appeared to be in a calmer state.
She may have been speaking to someone on a mobile phone, they said.
A third witness described a woman walking around the lake while typing on her phone.
Police have not been able to confirm the sightings were of Miss Croucher, and have urged anyone with information to come forward.
The search for the missing teenager has involved specialist police search teams, the mounted section, police dogs, the marine unit and the National Police Air Service.
Police have visited more than 4000 homes and interviewed 100 potential witnesses in the last two months, but said they have found no trace of her.
A huge team is also sifting through CCTV footage, and an anonymous donor has offered a £5,000 reward for information.
Chief Inspector Neil Kentish, deputy local policing area commander for Milton Keynes, said: “We are very eager to establish the identity of the person who was described to us by the three witnesses.
“Even if this person was not Leah, we would still like to speak to them so that we can eliminate the sightings from our enquiries.
“If you believe that you are this person, or you know who it was, please contact us as it will greatly assist with our investigation.
“I would like to take this opportunity to remind people of Leah’s appearance; she is white, slim, with below shoulder length brown hair and sometimes wears glasses.”
He added: “I still believe that someone, somewhere, has a vital piece of information which will help us to find Leah. If you have, and for whatever reason you haven’t already come forward, I would urge you to think of Leah’s family and contact the police.”
The teenager’s parents Claire and John Croucher said “getting up is the hardest thing to do each day”.
“It has now been 62 long and heartbreaking days since our beautiful, wonderful daughter Leah vanished into thin air,” they said.
“When Leah was first reported missing we honestly believed that she would be home very soon. But that hasn’t happened and as each subsequent day begins we are filled with despair that another night has come and gone and we have received no phone call or visit meaning that Leah is still missing.”
They added: “People ask us how we carry on and the truthful answer to that question is we just don’t know. We have no choice. Getting up is the hardest thing to do each day.
“But the hope that the day will bring us our daughter is what spurs us on.”