Aung San Suu Kyi is facing mounting pressure to punish troops accused of atrocities against Rohingya Muslims and her reputation has been tarnished over her handling of the crisis.
Mr Johnson and Ms Suu Kyi met after the Foreign Secretary visited Cox's Bazar, a huge refugee camp in Bangladesh where hundreds of thousands of Rohingya have fled after the army crackdown in Rakhine.
The UN has accused Buddhist-majority Myanmar, also known as Burma, of driving the Muslim minority over the border in an ethnic cleansing campaign, but the country has denied the charges.
UN investigators have been blocked from the conflict zone.
Doctors Without Borders (Medecins Sans Frontieres) estimates 6,700 Rohingya died in the first month of violence.
Fresh reports of mass graves and the arrest of two Reuters journalists investigating massacres have piled more pressure on Ms Suu Kyi to condemn the army, which she is in a delicate power sharing arrangement with.
She has refused to change tack.
Speaking after their meeting, Mr Johnson revealed he raised "a range of challenges facing her country".
He said: "I spoke to her about my own experience witnessing the terrible conditions of the Rohingya refugees in Bangladesh, and my deep concern about their future.
"I underlined the importance of the Burmese authorities carrying out a full and independent investigation into the violence in Rakhine, and to hold to account those responsible for human rights violations.
"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.
"The UK is already a major donor to the humanitarian crisis. We will continue to use all our diplomatic tools and influence on the global stage to find a way to provide a better future for the Rohingya community.
"I encouraged her efforts to broker a nationwide peace settlement to put to an end seventy years of conflict in her homeland."
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Following his meeting the Foreign Secretary travel to Rakhine, before going on to Bangkok for a two-day visit for meetings with junta chief Prayut Chan-O-Cha and the Thai chairman of an advisory board on the Rohingya crisis.
Before the meeting, Mr Johnson said: "The plight of the Rohingya and the suffering they have had to endure is one of the most shocking humanitarian disasters of our time.
"This is a man-made tragedy that could be resolved with the right political will, tolerance and cooperation from all those involved.
"I want to see and hear for myself the terrible things these people have been through, and I will be talking to State Counsellor Aung San Suu Kyi and other regional leaders about how we can work together to resolve this appalling crisis."