* Ex-PM Yingluck expected to meet military
* Her brother Thaksin is at heart of protracted crisis
* Army staged coup after talks between political groups failed
* Country appears calm after first night under curfew
* Stock market falls, baht currency recovers (Adds Yingluck expected to meet army, Prayuth to see king, markets)
By Amy Sawitta Lefevre and Robert Birsel
BANGKOK, May 23 (Reuters) - Thailand's military leaders summoned ousted Prime Minister Yingluck Shinawatra to a meeting on Friday, a day after army chief Prayuth Chan-ocha seized power in a bloodless coup and said he wanted to restore order following months of turmoil.
General Prayuth launched his coup after the various factions refused to give ground in a struggle for power between the royalist establishment and a populist government that had raised fears of serious violence and damaged Thailand's economy.
Soldiers detained politicians from both sides when Prayuth announced the military takeover, which drew swift international condemnation, after talks he was presiding over broke down.
Leaders of pro- and anti-government protest groups were still believed to be in detention on Friday, an opposition lawmaker said, declining to be named.
The military censored the media, dispersed rival protesters in Bangkok and imposed a nationwide 10 p.m. to 5 a.m. curfew.
It has summoned Yingluck and 22 associates, including powerful relatives and ministers in her government, to a meeting at an army facility at 10 a.m. (0300 GMT) on Friday.
Yingluck is the sister of Thaksin Shinawatra, a billionaire telecommunications tycoon turned politician who won huge support among the poor but the loathing of the royalist establishment, largely over accusations of corruption and nepotism. He was ousted as premier in a military coup in 2006.
Aides to Yingluck had arrived at the army facility by mid-morning and she was expected to follow.
Prayuth himself may not be present. He was expected to meet King Bhumibol Adulyadej on Friday at the royal palace in Hua Hin, in the south of the country, to explain the army's move.
Yingluck was forced to step down as prime minister by a court on May 7 but her caretaker government, buffeted by more than six months of protests, had remained nominally in power, even after the army declared martial law on Tuesday.
Any meeting could set the tone for army rule as Prayuth tries to steer the country out of crisis and fend off international criticism of the latest lurch into military rule.
Bangkok has remained calm and activity appeared to be relatively normal on Friday, although the military has ordered all schools and universities to stay closed.
Public transport was running after the curfew ended and early traffic was light, but cars were moving slowly on some roads into the capital because of army checkpoints.
Regular television schedules were suspended with all stations running the same news programme, featuring content from Channel 5, the army's own channel.
It showed pictures of the areas, now cleared, that had been taken over in and around Bangkok by various political groups since anti-government protests flared up last November.
Other footage showed people going about their business normally in cities around the country. Some were interviewed, saying they welcomed the coup.
U.S. Secretary of State John Kerry said there was no justification for the coup, which would have "negative implications" for ties with its ally, especially military ones.
"The path forward for Thailand must include early elections that reflect the will of the people," Kerry said in a statement.
He also called for the release of detained politicians.
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."
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.
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 sympathisers.
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.
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. (Additional reporting by Apornrath Phoonphongphiphat and Bangkok bureau; Writing by Robert Birsel and Alan Raybould; Editing by Alex Richardson)