The meeting took place at the Santi Maitri Hall of Government House.
Ms Yingluck, in her opening speech, said the government would act only as a coordinator of the political forum to which important figures who are rich with experience in many fields and hold different opinions have been invited to help formulate a solution to bring Thailand out of the political impasse and lay down a framework for the country's future.
She said it was pity not all of those invited had accepted the invitation, particularly the opposition Democrat Party and the PAD, adding that they are always welcomed to join later since the forum is open to all for their suggestions.
She also informed the meeting of a reconciliation forum to be held on Sept 2 to which several world-leading figures have been invited to be guest speakers to relate their experiences which can be useful for Thailand.
Among the very first to show up for the meeting were former prime ministers Chavalit Yongchaiyudh, Somchai Wongsawat and Banharn Silpa-archa.
Others who turned up were Bhichai Rattakul, a former Democrat Party deputy leader, Uthai Pimchaichon, a former parliament president, Gen Sonthi Boonyaratkalin, the Matubhum Party leader and former chairman of the Council for National Security (CNS), Anuthin Charnvirakul, the Bhumjaithai Party leader, Suwat Liptapanlop, a core member of the Chart Pattana Party, Payungsak Chartsuthiphol, chairman of the Federation of Thai Industries (FTI), Tida Tawornseth, chair of the red-shirt United Front for Democracy against Dictatorship (UDD), House Speaker Somsak Kiatsuranont and Senate Speaker Nikhom Wairatpanich.
Gen Chavalit said at the meeting that the people should have a bigger role and more power in the country's political reform agenda and the development of democracy.
He said despite past attempts to solve conflicts, the past military coups and constitutions being abolished and rewritten over and over again, there had been no serious mentioning of the people's sovereign power.
The people should be given a bigger role and more power, he said.
Gen Chavalit said he believed the political reform forum organised by the government would be useful and that proposals put forward would be put into practice.
On the announcement by the People's Alliance for Democracy's first-generation of leaders that they were quitting political activities and would give their supporters a free hand to take their own political course, the former prime minister said what the PAD leaders had done was also for society.
He believed they would continue to make other useful contributions for the country.
Tida Tawornseth, the chairwoman of the UDD, said the red-shirt group did not have a duty to protect the government but wanted the political reform forum to genuinely belong to the people, not just some 70 people invited by the government.
"I want to see this forum as a forum of the people of the whole country. The people's participation is essential," she said.
Ms Tida said the forum should not be used for groups in conflict to offer to take a step backward to bargain for their own interest. She added that "doing this would not offer a way out for the country".
"A way out for the country should enable the people with different political ideologies to stay together in peace," she said.
Uthai Pimchaichon, a former parliament president, said the forum should be divided into groups to look into the country's main problems over the economic, administrative and social systems.
The government should join hands with the private sector to tackle problems, he said.
Gothom Arya, an advocate for peace, said a council should be set up to study, manage and exchange opinions through social media.
Wuthisarn Tanchai, deputy secretary-general of King Prajadhipok's Institute, said a clear target should be set for solving problems.