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.
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.
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But the Nobel laureate has refused to change tack and is accused by critics of adopting a siege mentality.
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.
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.
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.