Gianni Alemanno said the Ara Pacis Museum, which encases a 2,000-year-old sacrificial altar, "will be removed".
The building, which sits alongside the River Tiber in the heart of Rome, is made of glass and travertine stone.
Richard Meier, who designed the project - finished in 2006 - said he was shocked by the comments.
"I don't know how serious he is," Mr Meier said from New York, adding that he would be ready to come to Rome to discuss the building with Mr Alemanno if invited.
The striking structure - which includes 500sq m (5,380sq ft) of glass - was one of the first pieces of modern architecture to be built in central Rome since the time of the dictator Benito Mussolini.
Mr Alemanno later conceded that it would be Rome's citizens who would decide whether or not to pull down the museum, saying he planned to hold a referendum on the subject.
"There's a problem of compatibility, the structure is surrounded by baroque buildings and, in that part of the city, any intervention must be in the same style," he said.
"It's not the most important priority but I think some of the building work there has been very invasive."
But despite, or perhaps because, of the controversy the Ara Pacis Museum has proved popular with tourists.
According to Italy's La Repubblica newspaper, some 6,000 people visited the museum in three days in April alone.
- Old Master
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I visited Rome a year back and was very dissappointed by the city in regards to modern architecture as a whole. I know that the city is very ancient and care has to be taken in inserting new buildings into the city fabric, but Rome seems totally devoid of modern architecture. Meiers building is very nice but there does seem to be a large lack of context, a problem with a lot of his work. Likewise it could be said that this building could have gone anywhere, like a lot of Meiers buildings.
Are we seeing another Prince Charles emerging in Italy? Lot of messed up politics in Italy at the moment.
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Of course the Roman city centre has few "modern" buildings. For all their faults, the Roman Heritage Authorities do have a sense of the importance of the city centre.
If you want modern architecture, there is PLENTY of it in the "periferia", as they call it. And, as I notice, not too many undertake the trip to see it!
- Old Master
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