* Army chief met political parties, rival protest groups
* Meeting inconclusive, said participants
* Army declared martial law on Tuesday, denies staging coup
* Acting PM says he is still in charge, has proposed Aug. 3 election (Adds U.S. comment, paragraphs 17-20)
By Panarat Thepgumpanat and Amy Sawitta Lefevre
BANGKOK, May 21 (Reuters) - Thailand's rival political factions would not agree to stop street protests on Wednesday during crisis talks aimed at ending the confrontation a day after the army declared martial law, a pro-government activist said.
Although the military denied Tuesday's surprise intervention amounted to a coup, army chief General Prayuth Chan-ocha appeared to be setting the agenda by forcing groups and organisations with a central role in the crisis to talk.
Issues raised during the meeting included reforming the political system - a demand made by anti-government protesters - and ending the demonstrations that have sparked violence, disrupted business and scared off tourists.
"When asked whether each group can stop protesting, there was no commitment from either side," Thida Thawornseth, a leader of the pro-government "red shirt" political group, told Reuters. "There was no clear conclusion."
Puchong Nutrawong, secretary-general of the Election Commission, who was also at the talks, said all sides would meet again on Thursday.
"The army chief asked us to go back home and think about the things we discussed in order to find a solution for the country," Puchong told Reuters.
Thailand has been riven for nearly 10 years by the rivalry between populist former Prime Minister Thaksin Shinawatra and the royalist establishment.
Thaksin, a former telecommunications billionaire who won the loyalty of the rural and urban poor, has lived in self-exile since 2008 but still exerts a huge influence, most recently through a government run by his sister, Yingluck Shinawatra.
Yingluck was forced to step down as premier by a court two weeks ago, but her caretaker government remains in power, despite the declaration of martial law and six months of sometimes violent protests aimed at ousting it.
The turmoil has driven the country to the brink of recession and even raised fears of civil war.
The anti-government protesters are opposed to an election, which Thaksin's loyalist would be likely to win. They want a "neutral" prime minister installed to oversee electoral reforms aimed at ending Thaksin's influence.
The government sees a general election as the best way forward and has proposed a new vote on August 3. The anti-government protesters disrupted an election in February that was later annulled, and they have vowed to do so again.
Whether all sides could accept an interim prime minister and what reforms could be implemented were also raised at the talks, Thida said.
An army spokesman said all sides would go away to think.
"There was no conclusion. It is as though homework was handed out for each side to work on," deputy army spokesman Winthai Suvaree told reporters.
Military sources say Prayuth is believed to favour the appointment of an interim prime minister by the Senate, who would then shepherd through reforms.
The United States, a close ally of Thailand and its military, said it was "encouraged" by reports that the meeting had taken place, although State Department spokeswoman Jen Psaki added: "Obviously, there is a great deal more work that needs to be done."
"Broadly speaking, we believe that dialogue between the parties is a positive step," she told a regular briefing.
"We continue to be troubled by restrictions on the media," Psaki added. "In our communications with the Royal Thai Army, we are encouraging them to respect democratic principles, including freedom of speech and the press."
Washington has stressed the need for the army to honour its commitment to make martial law temporary and Psaki reiterated that the United Stated wanted to see a return to full democracy.
Twenty-eight people have been killed and 700 injured since this latest chapter in the power struggle between Thaksin and the royalist elite flared up late last year.
Both pro- and anti-government protesters remain out in force, but the army has confined them to their separate protest sites and there were no reports of trouble overnight.
General Prayuth said he had imposed martial law to restore order, and the caretaker government says it is still running the country.
"Certainly, it's not an outright military coup by definition because the caretaker government is still in office, but on the ground it looks like the military is in charge," said Thitinan Pongsudhirak, a political analyst at Chulalongkorn University.
He said Prayuth needed to convince everyone with a stake in the outcome of the need for "reforms before and after elections".
"He's taking a lot of risk, Prayuth, because the imposition of martial law puts him in a very tight spot ... The longer we do not see a resolution, the riskier it will become for the army," Thitinan said.
The United States, which cut aid to its military ally after Thaksin was toppled in the most recent of Thailand's frequent military coups in 2006, called on the army to respect "democratic principles."
"We're watching the situation very closely. We expect that the Thai army will be true to its word when it says that this is not a coup and this is just a temporary injunction," said Pentagon spokesman Rear Admiral John Kirby.
Thaksin's "red shirt" activists have warned of trouble if the caretaker government is ousted, but some analysts saw the appointment of an interim prime minister as most likely, despite the threat of a backlash.
"With martial law in place, we believe violence could be contained," Pimpaka Nichgaroon, head of research at Thanachart Securities, wrote in a note.
The present administration has only limited authority and is unable, for example, to push through fiscal policies to support the stumbling economy.
Human rights groups have said the declaration of martial law was akin to a coup.
The army has ordered 14 satellite TV channels, both pro- and anti-government, to stop broadcasting and it has warned against the spread of inflammatory material on social media.
A bookshop in one of the city's glistening malls said it had been ordered to remove from its shelves eight books on politics.
But for most residents and visitors, life went on largely as normal.
"It hasn't made any difference to me and my plans," said Tsugio Kurosawa, a Japanese executive on a business trip to Bangkok, who had been in Indonesia during riots there in the late 1990s. "This is nothing compared to that."
Additional reporting by Pracha Hariraksapitak and by David Brunnstrom in Washington; Writing by Robert Birsel and Alan Raybould; Editing by Alex Richardson and Gunna Dickson