He was not available for comment but a pro-Thaksin activist in his hometown of Chiang Mai said there was no immediate plan to protest.
"As of now we will not head to Bangkok, no plans. We will follow today's situation closely first," said Mahawon Kawang, a red shirt leader in Chiang Mai.
"Everyone won't back down"
In a first round of talks on Wednesday, Prayuth had called on the two sides to agree on a compromise that would have hinged around the appointment of an interim prime minister, political reforms and the timing of an election.
But neither side backed down from their entrenched positions on Wednesday and again on Thursday, participants said.
"As we cannot find a way to bring the country to peace and everyone won't back down I would like to announce that I will take power. Everyone must sit still," Prayuth told the meeting, according to one participant who declined to be identified.
The army has also clamped down on the media, including partisan television channels, and warned people not to spread inflammatory material on social media.
Leaders of the ruling Puea Thai Party and the opposition Democrat Party, the Senate leader and the five-member Election Commission had joined the second round of talks on Thursday.
Acting Prime Minister Niwatthamrong Boonsongphaisan, who did not attend, told reporters before the talks that his government could not resign as its enemies were demanding as that would contravene the constitution.
"The government wants the problem solved in a democratic way which includes a government that comes from elections," he said.
Read MoreThai interim PM says aiming for Aug. 3 election
Yingluck was forced to step down as premier by a court two weeks ago, but her caretaker government, buffeted by six months of protests against it, had remained nominally in power.
Government officials were not available for comment after the coup announcement.
Thailand's gross domestic product contracted 2.1 percent in January-March from the previous three months, largely because of the unrest, adding to fears it is stumbling into recession.
But weary investors have generally taken Thailand's frequent political upheavals in their stride, and analysts said the impact on markets in Southeast Asia's second largest economy might not be too severe.
"It's back to the old days," said Christopher Wong, senior investment manager at Aberdeen Asset Management Asia in Singapore. "Probably with the military coming in there's a bit more stability. There may be a knee-jerk reaction ... but as the dust settles it is probably back to normal."
Thailand's SET index closed before the coup announcement, ending 0.2 percent higher. The index is up 8 percent this year. The baht weakened to 32.54 to the dollar after the coup announcement, from 32.38 earlier.
The anti-government protesters want to rid the country of the influence of Thaksin, who they say is a corrupt crony capitalist who commandeered a fragile democracy and used taxpayers' money to buy votes with populist giveaways.
They wanted a "neutral" interim prime minister to oversee electoral reforms before any new vote.
The government and its supporters said a general election that it would likely win was the best way forward and it had proposed polls on Aug. 3, to be followed by reforms.