The sculpture, a heart with the inscription '...greatest of all is love', stands in a park outside Oslo Cathedral.
It is the only memorial to the bombing of the government quarters and the Utøya massacre in Oslo and a place of remembrance for many who were affected by the attacks.
Lisbeth Kristine Røyneland, chairman of a support group for victims of the attack, is shocked by the news that the council planned to remove the sculpture.
"I think it is very strange, especially considering that we don't have an official memorial in Oslo yet. The heart should remain," Røyneland told Norway's Dagbladet newspaper.
"When I am in that part of the city, I often visit the heart. It is an important place for all who were affected by the terror on 22 July."
In a letter to the artist Espen Hilde, who made the heart shortly after the attacks in 2011, the church council said that it must be removed immediately.
"We have started work on improving the park, and a permanent 'memorial sculpture' is is not appropriate in the park," the council wrote, giving him a deadline of 1 September to remove the work.
After a protest from the artist and others, the council has agreed to leave the sculpture standing for now.
"The heart will not be removed on Tuesday this week. The artist has said that he won't do it and and we have taken note of that. The heart will stay for a little while longer, maybe a year. That's OK with us," Robert Wright, a member of the council, told Dagbladet. "But it cannot be there forever. We are very clear about that."
Labour Party youth leader Mani Hussaini said he hoped the sculpture could stay.
"I don't know the details of the plan to develop the park at the Cathedral, but I hope that the sculpture can stay there in future. If the sculpture is removed I hope it can be placed somewhere else so that people can continue to put down flowers and light candles."