Johnson met with the embattled Myanmar leader, whose reputation among the international community has crumbled over her handling of the Rohingya crisis, in the capital Naypyidaw while on a four-day tour in Asia.
The meeting followed Johnson's visit to a refugee camp in Bangladesh's Cox's Bazar district, where nearly 700,000 Rohingya have sought sanctuary after fleeing a Myanmar army crackdown launched in northern Rakhine last August.
The UN has accused Myanmar security forces of driving the Muslim minority across the border in an ethnic cleansing campaign. Doctors Without Borders estimates at least 6,700 Rohingya died in the first month of violence.
But Myanmar has staunchly denied the charges and blocked UN investigators from the conflict zone, souring relations with a host of western allies.
Fresh reports of mass graves in Rakhine -- and the arrest of two Reuters journalists investigating an alleged massacre -- have heightened pressure on Suu Kyi to condemn the army, who she is in a delicate power-sharing arrangement with.
But the Nobel laureate has refused to change tack and is accused by critics of adopting a siege mentality.
On Sunday Johnson and Suu Kyi "discussed in an open and friendly manner the latest developments in Rakhine State, including planning for the reception of returnees who fled", Myanmar's foreign ministry said in a Facebook post alongside photos of the pair meeting.
Johnson, who later flew to Rakhine state, wrote on Twitter that he raised the "importance of (Myanmar) authorities in carrying out full & independent investigation into the violence in Rakhine".
He said he also stressed the "urgent need to create the right conditions for Rohingya refugees to return to their homes in Rakhine".
Myanmar and Bangladesh have inked a deal to bring back refugees, but repatriation has yet to begin.
Many Rohingya do not feel safe returning to a country where they have faced violent persecution and decades of discrimination at the hands of a state that has denied them citizenship.
Others have no home to return to after their villages were torched in the military crackdown.
After months of denying any abuses by its troops, Myanmar's military admitted in January that security officers had assisted with the killing of 10 Rohingya men in Rakhine's Inn Din village.
That public admission followed the arrests of the two Myanmar journalists who were investigating the massacre and are now facing up 14 years in prison on charges of possessing secret documents.
Johnson is scheduled to fly on to Bangkok later Sunday for a visit that will include meetings with junta chief Prayut Chan-O-Cha and the Thai chairman of an advisory board on the Rohingya crisis.
The panel was thrown into the spotlight last month after veteran US diplomat Bill Richardson published a withering resignation letter saying he could not in "good conscience" sit on a board he feared would only "whitewash" the causes of the Rohingya crisis.
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