John Kerry said the US's relationship with Egypt is "very important" as he visited the country for the first time since former president Mohamed Morsi was ousted.
The US Secretary of State said he had discussed with Egypt's foreign minister the need to end violence and have a constitution that "protects the interests of all all Egyptians".
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Ms Leadsom has received the backing of Ian Duncan Smith, the former work and pensions secretary.
The former shadow work and pensions secretary is considered a more viable candidate than Angela Eagle, a Labour source has told ITV News.
As many as 10 people have been rescued following the raid, according to a Bangladeshi official.