Planter boxes in the roads around Hyde Park were put in place to reduce rat running, cut pollution and make streets safer for pedestrians and cyclists.
But the idea has been met with strong opposition by some in the community.
A petition to abolish the scheme has received more than 800 signatures.
The planters have already been subject to vandalism, and cars have regularly been spotted mounting the pavement to get round the planters at Royal Park Road.
The closures in Royal Park Road and Alexandra Road have now been removed, but the rest will remain the six month trial period, according to the three councillors for the area.
Yacob Ahmed, who started the petition and has lived in Hyde Park all his life, said: “LTNs are not a good fit 'one size fits all' solution for the area of Hyde Park.
"The dynamics of the area and the landscape make it wholly incompatible and their effects absolutely counter intuitive.
"The councillors implementing the scheme are completely out of touch with the needs of the locals and the issues we have in the area and the ideas we've proposed to tackle the problems are not being listened to."
Nathan Clark, of Brudenell Social Club, said on social media: "The LTN initiative has caused utter chaos in our community.
"It was poorly consulted, poorly advertised and signposted. It has been badly thought about from traffic management. We support positive change not this!"
People who have signed the petition claim the scheme has made congestion worse and say local businesses are suffering.
Other criticisms include lack of consultation and the impact on emergency service vehicles - with others saying the city needs a mass transit system to tackle congestion.
All residents affected were written to and the emergency services have been consulted as part of the process in terms of access, according to the councillors.
Headingley and Hyde Park councillors Al Garthwaite, Neil Walshaw and Jonathan Pryor posted an update to their Facebook page.
They said: "This is a controversial scheme, and we know there are passionate views on both sides.
"We have a received a large amount of correspondence from people who are real fans of the scheme, feel safer, and appreciate the removal of air pollution from residential areas.
"We also have received a number of e-mails from people who do not like the scheme, and have had issues caused with local businesses."
They said Royal Park Road and Alexandra Road would be reopened "within the next few days".
They added: "This will be done within the next few days, while the rest of the planters will remain in place for the duration of the 6 month trial period.
"These two roads have been chosen as an arterial route through Hyde Park - while the other planters essentially turn the most heavily residential areas into a series of cul-de-sacs.
"We are aware of how dangerous crossing the junction of Royal Park Road and Queens Road can be however, so we will be monitoring this, as well as Alexandra Road, closely and seeing what other measures could be put in place here."
The councillors said they had received requests from other areas for similar schemes, which they would be looking in to.
They added: "Our plan remains to evaluate the entire scheme at the end of the 6 month trial, taking into account all feedback, positive and negative.
"This will most likely end in a compromise solution because we want the final scheme to be one the local community can get behind."
Responding to a question on a Facebook Live stream from someone against the scheme, Leeds North West MP Alex Sobel pointed out that he had not been consulted about the planters, but called for time for them to "bed in".
He added: "The idea really is around trying to create a better street scene, improve road safety, cleaner air - which are all things I agree with.
"What may be the best thing to do is for them to bed in a little bit, and see what the behaviour change is and for us to do a review of them."
Mr Sobel said it was not a matter of either removing them all or leaving them all in place.
He added: "Maybe some of them, after review, should be removed, and maybe some of them work very well and should stay in."
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