He said: "It is vital that the Rohingya refugees must be allowed to their homes in Rakhine voluntarily, in safety and with dignity, under global oversight, and when the conditions. are right".
He continued: 'I underlined the urgency of creating the conditions in Rakhine that could make it a safe place for the Rohingya refugees to return to, free from fear, and in the knowledge that their basic rights will be respected and upheld.
On Saturday, Johnson visited Cox's Bazar in Bangladesh to hear first hand accounts of suffering by the members of the mostly Muslim minority at the hands of Myanmar security forces.
"I pay tribute to the hospitality and compassion shown by the government of Bangladesh, who are facing an enormous challenge in providing humanitarian assistance to the Rohingya community".
Earlier Mr Johnson met Bangladeshi Prime Minister Sheikh Hasina and Foreign Minister Abul Hassan Mahmud Ali.
A month after the journalists were detained, Myanmar's army issued a rare statement taking responsibility for the deaths but claimed that those killed were "Bengali terrorists", reflecting the regime's official stance that the Rohingya are interlopers from neighboring Bangladesh.
The United States and the United Nations have called the military campaign against the Rohingya "ethnic cleansing".
Johnson and Aung San Suu Kyi "discussed in an open and friendly manner the latest developments in Rakhine State, including planning for the reception of returnees who fled", the Burmese Ministry of Foreign Affairs said in a Facebook post.
"This once more attests to the need for a full and thorough investigation by the authorities of all violence in Rakhine State and attacks on the various communities there", United Nations spokesman Farhan Haq told reporters in NY.
The Foreign Secretary stopped in Myanmar as part of a four-day trip to Asia, which will also include a visit to Thailand.