Pro-Russian rebels have said the death toll during two days of fighting in the eastern Ukraine city of Donetsk has now risen to 50.
The prime minister of the rebels' self-styled Donetsk People's Republic (DNR) Alexander Borodai told Russia's RIA news agency: "We have lost more than 50 volunteers."
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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.