But the council is to set up a group to "resolve outstanding design issues".
The proposed cycle route will link Leith Walk in the east of the city to Roseburn in the west, via the city centre and Haymarket.
The plans include reducing four lanes of traffic from Roseburn to Haymarket to two, and using half a carriageway and a bus lane for cyclists.
Supporters of the path said it was vital for cutting congestion and would provide a safe route across the city. They said it would also encourage more active travel.
But residents and shop owners in the Roseburn area said reducing loading bays to make way for bikes would have a huge impact on passing trade, and that reducing traffic lanes could increase congestion at Roseburn.
The council said the new working group would be set up to help resolve outstanding design issues with the plans.
It said work would start immediately to secure further funding and to "make preparations to commence the necessary statutory processes for the scheme".
A final decision will be taken after the the working group's discussions.
Transport convener Councillor Lesley Hinds said the council was still "100% committed" to the project but acknowledged it had divided opinion.
She said a new group would be formed to try to reach a conclusion on the final route design "which the majority are happy with".
Ms Hinds added: "Given the strength of feeling out there about certain aspects of the plans, there's clearly still work to be done before the final route design is agreed."

The pavilion and green from Billingham's John Whitehead Park are to form part of the 1950s town in Beamish open air museum.
Once it is complete, visitors will be able to try their hand at bowls and discover stories of the popular leisure pursuit and wider community life.
The Â£10.7m 1950s development will also include an original house, shop and cinema from the era.
Beamish is also seeking people's memories of the bowling pavilion, and staff will be attending an open day at the Billingham Bowling Club on Sunday.
Geraldine Straker, of Beamish, said: "We'll be telling the story of life in the region's tight-knit communities, and clubs such as this played an important part.
"We really want to hear people's memories of life in the 1950s, particularly any early memories of the bowling pavilion, and this will help shape the stories we share at Beamish."

Jordan Hill, Brittany Covington and Tesfaye Cooper, all 18, and Tanishia Covington, 24, appeared in a Chicago court on Friday.
The four have been charged with hate crimes and aggravated kidnapping and battery, among other things.
An online fundraiser for their victim has collected $51,000 (Â£42,500) so far.
Denying the four suspects bail, Judge Maria Kuriakos Ciesil asked: "Where was your sense of decency?"
Prosecutors told the court the beating started in a van and continued at a house, where the suspects allegedly forced the 18-year-old white victim, who suffers from schizophrenia and attention deficit disorder, to drink toilet water and kiss the floor.
Police allege the van was earlier stolen by Mr Hill, who is also accused of demanding $300 from the victim's mother while they held him captive, according to the Chicago Tribune.
The court was also told the suspects stuffed a sock into his mouth, taped his mouth shut and bound his hands with a belt.
In a video made for Facebook Live which was watched millions of times, the assailants can be heard making derogatory statements against white people and Donald Trump.
The victim had been dropped off at a McDonalds to meet Mr Hill - who was one of his friends - on 31 December.
He was found by a police officer on Tuesday, 3 January, a day after he was reported missing by his parents.
Prosecutors say the suspects each face two hate crimes counts, one because of the victim's race and the other because of his disabilities.
Plans for a controversial cycle path through Edinburgh have been agreed in principle by city councillors.
[NEXT_CONCEPT]
A Teesside bowling club is being replicated at a County Durham museum.
[NEXT_CONCEPT]
Four people accused of kidnapping and torturing a mentally disabled man in a "racially motivated" attack streamed on Facebook have been denied bail.