Details of his discussion with Prayuth were not immediately available.
Thai Foreign Minister Don Pramudwinai, who also met with Johnson, told reporters that the British government is especially concerned about the plight of the Rohingya.
About 700,000 members of the Muslim minority have fled to Bangladesh to escape violence by Myanmar security forces that has been characterised by some human rights experts as ethnic cleansing.
In Myanmar, Johnson also visited areas in the western state of Rakhine, the site of the violence that drove the Rohingya to flee.
Plans to repatriate the Rohingya have been made by Bangladesh and Myanmar, but are a major concern of the international community. Human rights advocates insist that any repatriation be carried out under verifiably safe conditions.
"Shocked at what I saw during tour of northern #Rakhine," Johnson wrote on Twitter.
"In the eyes of the British government right now, they are putting an emphasis on fixing the issue of Rohingya in Rakhine state, first and foremost," Don said, adding that Britain did not ask for the Thai government's help in the matter.
Thailand's military seized power from an elected government in 2014. Boris Johnson's visit today follows a European Union decision last December to ease political sanctions on Thailand imposed after the coup.
"They are not pressuring Thailand to hold elections because they do not see it as having any impact on England," Don said.
Johnson's visit to Thailand came after an official visit last Friday by Italy's foreign minister, and will be followed by the French deputy foreign minister tomorrow.
Thai Foreign Ministry spokeswoman Busadee Santipitak said last Friday that the trips are a sign of improved relations between Thailand and European nations following the EU's easing of sanctions.
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