The US military has cancelled training exercises with Thailand, as well as a visit to the Asian nation.
Pentagon Press Secretary Real Admiral John Kirby said: "As we have made clear, it is important that the Royal Thai Armed Forces end this coup and restore to the people of Thailand both the principles and the process of democratic rule, including a clear path forward to elections."
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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.