Serious concerns have been raised about the safety of Hearts' new main stand at Tynecastle Park.
Police Scotland have written to Edinburgh City Council asking for the club's safety certificate to be re-examined after they identified numerous concerns now the stadium is back in use.
The concerns centre on crowd safety and movement, leading to the possibility of pitch invasions and a build-up of spectators in several areas.
There is potential for increased tension and risk around where officials are positioned, the letter states, with the directors' box having "no delineation from the rest of the stand".
Hearts closed the stadium for redevelopment and the construction of a new stand to replace the previous 103-year old structure.
The reopening of Tynecastle was delayed and a safety certificate was granted the day before Hearts played Partick Thistle on November 19.
In the letter to Edinburgh City Council's public safety department, Police Scotland listed issues they are concerned about.
Three matches have now been held at the stadium.
The police superintendent responsible for events in the city, wrote: "At present, I have concerns over the public safety of patrons attending football matches at Tynecastle Park."
The letter detailed a problem before the match against Partick Thistle when turnstiles failed, leading to lengthy queues and a delayed kick-off.
An incident before the Hamilton fixture last weekend, when a kitchen sensor triggered a fire alarm, also delayed the start of a match.
The superintendent also raises issues about lighting.
He said: "Given the incidents in the previous three matches I now have significant concerns over the reliability of electrical systems within Tynecastle Park.
"Electrical failings impact on public safety with evacuations and delayed kick-offs as evidenced in recent matches."
The superintendent said the likelihood of emergency or evacuation was significantly increased.
With four matches scheduled for the stadium over the next month, police requested "that the City of Edinburgh Council re-examine the safety certificate issued to Heart of Midlothian FC for Tynecastle Park and undertake whatever investigation that you deem necessary to address the points above and ensure a safe and reliable stadium".
Chief superintendent Kenny MacDonald, divisional commander for Edinburgh, told STV: "Police Scotland plays an active role in the safety advisory groups across Scotland, which have responsibility for event safety.
"I can confirm that Edinburgh Division has written to the City of Edinburgh Council in relation to spectator safety at a football ground.
"The safety of the public attending sporting events is paramount and there are robust processes in place by football clubs, the police and the local authority and other partners to ensure safety is our number one priority.
"We continue to work with all relevant partners to ensure that any future events are safe for the public to attend."
A spokesperson for the City of Edinburgh Council, said: "The safety of everyone attending matches is paramount and the council is working with Hearts and their contractors to ensure that the matters raised by Police Scotland are addressed.
"As work in the stadium is ongoing, contingency measures are being put in place to reinforce safety procedures, while temporary occupation certificates and general safety certificates will continue to be issued on a match-by-match basis."
Hearts have confirmed the club was contacted by Edinburgh City Council regarding Police Scotland's concerns, but say Saturday's match will go ahead following a satisfactory meeting between all parties at Tynecastle.
A statement from the club read: "Heart of Midlothian Football Club can confirm that it was contacted by Edinburgh City Council with regards to a letter sent to them by Police Scotland.
"The letter expressed some concerns regarding general security following a number of unrelated incidents at the first three games held at Tynecastle Park.
Following a satisfactory outcome to a meeting held today at the stadium, attended by all parties, the club is looking forward to welcoming Motherwell Football Club to Tynecastle Park this Saturday."