The zoo said that implantation, when the fertilised egg attaches to the uterus, has not yet taken place and said it could be months whether it is known if a full pregnancy has occurred.
Iain Valentine, director of giant pandas for the RZSS, said: “Scientific data does suggest Tian Tian has conceived, however this is not pregnancy. Giant panda pregnancies are extremely complex.
“Pregnancy begins when implantation takes place and this has not yet occurred. There are many hurdles to get through yet, so we would request that people do not get too excited at this very early stage.”
Tian Tian, which translates as Sweetie, was artificially inseminated in March, ahead of an attempt at natural mating between the female and Yang Guang, which means Sunshine, who were brought to Edinburgh from China nearly four years ago. The insemination was carried out by a team of three vets, alongside a panda expert from China.
Two previous attempts at mating – which can only take place at one specific time of year when hormone levels are at a peak – have been unsuccessful.
Breeding pandas is notoriously difficult, both in getting them to become pregnant and carrying the cub to full term. Both Tian Tian and Yang Guang have bred before, although not with each other.
Giant pandas practice “delayed implantation” which means the egg is not attached until late on in the pregnancy, unlike humans and also often have phantom pregnancies.
It is likely to be late July or August before experts know whether the panda, who has lost her last two pregnancies, is actually pregnant. If she is carrying a cub, it would be likely to be born in August or September.
The pair, who are generally solitary and only meet when mating, are the first giant pandas to live in the UK for 17 years.
Malcolm Roughead, chief executive of VisitScotland, said a panda cub would be a major tourism draw for Edinburgh – and Scotland.
He said: “Edinburgh Zoo is one of Scotland’s most popular paid-for attractions and following the arrival of Tian Tian and Yang Guang visitor numbers have rocketed.
“If Tian Tian does become pregnant and goes on to have a healthy cub, excitement will intensify and images of Edinburgh Zoo will be seen across the world. This will generate a real buzz not only around the zoo, but also around Edinburgh and Scotland as a whole.
“This global media attention is an excellent way to introduce the country to new and potential visitors from all across the globe.”
The pandas, which are on loan from China for a decade for an annual fee of £600,000, have boosted visitor numbers at the zoo, pushing profits 53 per cent higher within the first year.