He also said Paris is "no longer the same city it was".
The mayor of London said the comments were "complete and utter nonsense".
A Metropolitan Police spokeswoman said: "We would not normally dignify such comments with a response, however on this occasion we think it's important to state to Londoners that Mr Trump could not be more wrong.
"Any candidate for the presidential election in the United States of America is welcome to receive a briefing from the Met Police on the reality of policing London."
Mayor Boris Johnson said the remarks were ill-informed.
"As a city where more than 300 languages are spoken, London has a proud history of tolerance and diversity and to suggest there are areas where police officers cannot go because of radicalisation is simply ridiculous," he said.
Mr Johnson said police officers were doing "excellent work" in London.
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