The Myanmar government has faced global accusations of waging an ethnic cleansing campaign in Rakhine, with almost 700,000 Rohingya fleeing the area since last August amid reports of atrocities committed by troops and vigilante groups.
Johnson toured a camp that has taken in some of the estimated 650,000 Rohingya who fled from violent attacks past year.
Myanmar has staunchly denied the charges and blocked United Nations investigators from the conflict zone, souring relations with a host of western allies.
Doctors Without Borders (Medecins Sans Frontieres) estimates 6,700 Rohingya died in the first month of violence.
She has refused to change tack.
Boris Johnson has been visiting camps on the Bangladesh border that hold the refugees who fled Myanmar to escape a military crackdown.
Reuters on Friday published a report laying out events that led up to the killing of 10 Rohingya men in the northern Rakhine village of Inn Din who were buried in a mass grave after being hacked to death or shot by Buddhist neighbours and soldiers. "The investigation was being conducted even before Reuters news", Zaw Htay said, adding that he was unable to specify what action would be taken against the 16 people.
Mr Johnson is due to tour Rakhine State with representatives from the Burmese military later. And we are not giving blanket denials."If there was "strong and reliable primary evidence" of abuses, the government would investigate, he said".
"Discussed importance of Burmese authorities in carrying out full & independent investigation into the violence in #Rakhine & urgent need to create the right conditions for #Rohingya refugees to return to their homes in Rakhine", Johnson wrote on his Twitter account of his meeting with Suu Kyi, who also serves as foreign minister.
Johnson is scheduled to fly on to Bangkok today for a two-day 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 United States 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.