Police are continuing inquiries into the death of Jodie Muir, a pupil at Eastbank Academy, Shettleston, who died following a party in Rutherglen on Friday night.
Relatives have said on social media sites that the youngster had a heart condition, Long QT syndrome.
Gordon Shaw, head teacher of Eastbank Academy, said: "This is tragic news and our thoughts and prayers are with Jodie's family and friends at this very sad time.
"Jodie was a popular and valued pupil, and we will be offering any support that is needed to her classmates and teachers."
Youngsters left scores of bouquets and balloons for the teenager at the gates of the school.
Dozens of friends left flowers and teddy bears, and a huge cardboard sign was left among the tributes to allow friends to leave messages of condolence.
The youngster had returned home from the party at about 5am on Saturday and died several hours later.
Police said they had spoken to a "significant" number of the 40 to 50 teenagers believed to have been at the party.
Initial reports claimed Jodie had taken an ecstasy-type tablet at the party, but relatives have refuted the claims.
Tests are being carried out to establish the cause of death.
Ciorstan Shearer said: "I do not yet know whether drugs have played a part in this tragic death and it is therefore important to trace other party-goers.
"It is vital that those who have not already spoken to police come forward as soon as possible, to ensure they are safe and well, but also because they may provide vital information.
"I urge anyone who was at the party and has taken drugs and is feeling unwell to attend or contact their local hospital for treatment or advice.
"Anyone with information is asked to call London Road police office on 101."