One firearms officer is believed to have suffered a broken wrist while the suspect in Edmonton was being detained, police said.
Police added that a stun gun was discharged during the operation.
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Political parties across the country suspended their General Election campaigns following the Manchester Arena terror attack on Monday.
Investigators believe Mr Kushner has significant information relevant to their inquiry, officials told NBC News.
The men were detained as part of an investigation by MI5 and the Metropolitan Police's Counter Terrorism Command.