Sheffield City Council is to call a temporary halt to its tree replacement programme.
Campaigners claim the council has cut down a number of healthy trees among the thousands felled since 2012.
The BBC's Dino Sofos told the Daily Politics show there would be "no felling for the next few weeks".
The council said contractor Amey was "exploring options for completing the work and will present these options to the council".
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The news comes after Environment Secretary Michael Gove said he would do "anything required" to stop the work.
In a statement, the council said: "In the past year or so the actions of a handful of people unlawfully entering the safety zones where tree replacement work is being carried out has meant that it has become increasingly difficult for Amey to complete the programme without danger to staff and members of the public."
The council added during the review period "only trees which are dangerous will be worked on".
The felling is part of the £2bn 25-year Streets Ahead project, which is being carried out by contractor Amey and has seen about 5,500 trees removed since 2012.
The council says the trees have been assessed as dead, dying, diseased, damaging or dangerous, and each tree cut down will be replaced.
However, campaigners say healthy trees have also been lost.
The dispute has led to a series of stand-offs between protestors, contractors, private security staff and police, with a number of campaigners arrested and a court injunction imposed as a result.
Speaking on the BBC's Daily Politics, Conservative MP for Chichester Gillian Keegan said: "It does seem ridiculous. The whole country is covered with tree-lined streets that have these problems with roots and trying to keep flat pavements.
"This is something every other council deals with. What on earth is happening [in Sheffield], to have police on the streets, for this to have escalated in to such a big deal? This happens day in, day out across the country."