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"We should all urge calm and respect for laws, institutions, and basic human rights and freedoms - and support for the democratically elected civilian government," the statement read in part.
Clinton's words appeared to echo those of President Barack Obama, who issued a statement earlier Friday, saying "all parties in Turkey should support the democratically elected government of Turkey, show restraint, and avoid any violence or bloodshed."
Dozens were reportedly killed and many more were injured during the uprising.
The violence in Turkey comes just a day after an unprecedented attack in the south of France, where at least 84 people were killed as festivities were underway in celebration of Bastille Day.
Here's Clinton's full statement on Turkey:
"I am following the fast-moving developments in Turkey tonight with great concern. We should all urge calm and respect for laws, institutions, and basic human rights and freedoms - and support for the democratically elected civilian government. All parties should work to avoid further violence and bloodshed, and the safety of American citizens and diplomatic missions must be ensured."