There was also condemnation from France, the European Union and the United Nations human rights office. Japan said the coup was regrettable and Australia said it was "gravely concerned."
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Prayuth is a member of the royalist establishment generally seen as hostile to the Shinawatras, although he has tried for months to keep the army out of the political strife and to appear even-handed.
He enjoyed cordial relations with Yingluck after she took office following a landslide election victory in mid-2011 but is regarded warily by some Thaksin supporters.
The army chief, who is 60 and due to retire later this year, has taken over the powers of prime minister but it was not clear if he intended to stay in the position.
Market reaction muted
The anti-Thaksin protesters had demanded electoral changes that would end the Shinawatras' success at the ballot box. Thaksin or his parties have won every election since 2001.
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Thaksin's "red shirt" supporters were dismayed and angry but said they had no immediate plans for protests that they had threatened in response to any army takeover. Those who had been protesting in Bangkok dispersed peacefully after the coup.
Protests would be a major test for Prayuth, who commands an army known to contain some Thaksin sympathizers.
In 2010, more than 90 people were killed in clashes, most when the army broke up protests against a pro-establishment government that had taken office after a pro-Thaksin administration was removed by the courts in 2008.
Weary investors have generally taken Thailand's upheavals in their stride and the baht was slightly firmer in early trade at around 32.50 per dollar. It had weakened to 32.70 in offshore trade after the coup.
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The stock market fell 2 percent in early trade after ending 0.2 percent higher on Thursday before the coup news. Local investors had taken the view that the martial law imposed on Tuesday might bring some stability to the country.
Thailand's economy contracted 2.1 percent in the first quarter of 2014 from the previous three months, largely because of the prolonged unrest, which has frightened off tourists and dented confidence, bringing fears of recession.