City authorities said they had stopped the destruction as a sign of good will after riots followed Monday's eviction of residents from Can Vies, a public building facing demolition after being occupied for nealy two decades by leftist groups in Barcelona.
Clashes between police and protesters have led to dozens of arrests over four nights. On Thursday night alone, 23 people were arrested and five were injured.
"The Council is maintaining its commitment to finding a joint solution that satisfies all parties," municipal authorities said in a statement about the unrest which has captured nationwide attention.
The city said it was "possible to find solutions" so that Can Vies could continue to carry out its cultural work, but condemned all violence.
"Any protest or gathering in the city must be peaceful," the town hall said.
The decision by Barcelona's town hall to stop demolition of the building comes after the Can Vies collective on Friday called for the resignation of city mayor Xavier Trias and the local councillor for the district of Sants-Montjuïc, Jordi Martí.
The collective also demanded a stop to demolition of the building, the withdrawal of police from the area, and the release of all protesters who had been arrested.
The group have been supported in their battle to save the building by a group of elderly protesters known as 'iaioflautas'.
These protesters — the word is a blend of the Catalan term 'iaio', meaning gramps, and 'perroflauta' or hippy — have occupied the entrance way of Barcelona's town hall to demonstrate against the closure of the centre.
The Can Vies house in the working-class Sants neighbourhood is owned by the city transport authority but was occupied in 1997 by activists who used it to host concerts, training courses and other community activities.
The transport authority wants to knock it down to redevelop the area, where a rail and metro line intersect.
On Monday, police cleared the house following a court order issued after negotiations broke down between the city and the squatters.