On an official visit to the US June 11-16 to boost the longstanding relations between the two countries, Mr Surapong had urged the US government to lift all sanctions imposed against Myanmar in order to demonstrate that the country has stepped onto the right path.
The Thai foreign minister said he advised the US to give equal importance to Myanmar President Thein Sein and Myanmar opposition leader Aung San Suu Kyi, for the two could lead to the country's reconciliation.
The US secretary of state however said the total lifting of sanctions on Myanmar could not be possible as it must get through the complicated American legal procedures. Therefore, it should be gradually lifted, Mr Surapong said.
The bilateral talks included the two countries' cooperation on prevention of terrorism, drugs, international crime, as well as on investments, particularly under the Trans-Pacific Partnership (TPP).
Scheduled to participate in an ASEAN ministerial meeting in Cambodia's Phnom Penh next month, Mrs Clinton said she wished the Thai prime minister will join in the event. During such an occasion, Mr Surapong invited his counterpart to visit Thailand and asked the United States to invite Thai premier Yingluck Shinawatra to visit the US in July or August for further exchanges and memorandums of understanding (MoUs) on different issues.
There was also a discussion of an official visit between the US President Barack Obama and the Thai prime minister.
According to the Thai foreign minister, tripartite cooperation between the US, Thailand, and Myanmar will take place to assist Myanmar on different matters. Further discussion and details of the memorandum of understanding (MoU) will be made later today, where the two countries are holding a strategic meeting covering several areas.
Thailand and the US wish to develop their relations and cooperation for the benefit of both countries' peoples and of prosperity in the region and the world.
Lastly, Thailand asked the US to continue supporting displaced persons fleeing fighting in Myanmar to seek shelter in Thailand.
Meanwhile, Mrs Clinton said she was proud of the record of 179 years of bilateral relations, noting that the United States supported Thailand to keep peace and prosperity in the area. The June 14 meeting is covering investment, peace, human rights, natural disaster assistance, and the relations between the peoples, according to Mr Surapong.
The Thai foreign minister met earlier the same day with Jim Webb, senior US senator from Virginia, a Democrat, and Jim Inhofe, senior US senator from Oklahoma, a Republican.