The 24-year-old woman died in hospital on Wednesday morning after she was hit by a bus shortly after falling into its path when her bike wheels got caught in a tram track on Princes Street.
Now city leaders in Edinburgh are looking to investigate how existing plans to improve safety could be accelerated.
Adam McVey, SNP group leader in the city, said the incident had been a “profound tragedy” and that he had spoken with council officers about potential changes.
He said: “It was deeply saddening for everyone in the city and my heart goes out to the family and friends of the women who lost her life.
“Events like this bring home just how vulnerable cyclists can be on our roads and emphasise how important new infrastructure and safety measures are to improve conditions for cyclists.
“I’ve spoken to senior officers about their immediate plans to improve cyclist safety, particularly on Princes Street, and about how we can accelerate some plans already in the pipeline to help improve safety for those on bikes across the city.”
It is understood parts of the capital’s planned East-West cycle route, which will be segregated in parts, are among measures which could be sped up.
First Minister Nicola Sturgeon yesterday sent her “heartfelt sympathies” to the 24-year-old woman’s family and friends, saying the incident was “sad almost beyond words”.
Ms Sturgeon said the Scottish Government was assisting investigations into the incident in any way it could and highlighted that she had increased investment in cycle safety.
She added: “The relevant minister would be willing to meet with cycling groups, not just in Edinburgh but across the country, to look at what further action we can take to make sure cycling, which is an activity we want to encourage, is as safe as it possibly can be for everyone who partakes in it.”
Some 200 cyclists have been injured by tram tracks in Edinburgh, with Lothian cycle campaign group Spokes saying urgent action was needed.
Brenda Mitchell, a senior partner at legal firm Cycle Law Scotland, said the young woman’s death could have been avoided, and called for an inquiry.
She said: “Spokes have come up with numerous recommendations time and time again and the time for paying lip service to this has got to end. We need serious action.”
A city council spokesman said: “We will carry out a road safety assessment of the area, considering all users and aspects of the junction and its approaches. The council and our partners take road safety extremely seriously.”