Foreign Office minister Mark Field has told Aung San Suu Kyi to end violence in Rakhine State and grant full humanitarian access.
But Mr Field said the country's de facto leader was in a "difficult position", with public opinion in Myanmar "strongly anti-Rohingya".
And Aung San Suu Kyi was Myanmar's "best hope for ongoing democracy".
More than 400,000 Rohingya have fled across the border to Bangladesh amid reports of military atrocities.
Ms Suu Kyi, the former political prisoner who has been Myanmar's civilian leader since winning elections in 2015, is under growing international pressure over her handling of the crisis.
In a speech on Tuesday, the Nobel Prize winner condemned human rights abuses but did not blame the army or address allegations of ethnic cleansing.
Mr Field held face-to-face talks in the capital, Nay Pyi Taw, becoming the first foreign minister from outside the region to meet Aung San Suu Kyi since the crisis began, and visited Bangladesh on Thursday to see the relief effort there.
Speaking to the BBC from Bangladesh, he said he had witnessed "heartbreaking" scenes of human suffering.
"It's a more complicated situation out there," he said.
"There has been a lot [of] inter-communal dispute that goes back some decades."
But he said: "Let's make no mistake: the humanitarian misery that we see there today is very largely the fault of the security forces."
Mr Field said he had told Aung San Suu Kyi "the violence must stop" and she should allow access to humanitarian aid - although public opinion in Myanmar, formerly known as Burma, had left her "in a difficult position".
"Under the constitution, the military remains very powerful. There are only small steps that have taken place in recent years towards democracy.
"And she finds herself treading a fine line between the international criticism... but also public opinion in Burma, which is and remains very strongly anti-Rohingya."
The BBC's South East Asia correspondent, Jonathan Head, said: "Public opinion in Myanmar is incredibly blind to what is happing in Bangladesh.
"There has been a huge upsurge of nationalist support for the army and a huge amount of anti-Muslim prejudice and a belief that the Rohingyas brought this on themselves.
"It's incredible how widespread that is."
Speaking on Wednesday, Labour leader Jeremy Corbyn appealed to Aung San Suu Kyi, as a "champion of democracy and human rights", to act now to put a stop to the violence.
"The Rohingya have suffered for too long," he told activists at his party's conference.
A stateless mostly Muslim minority in Buddhist-majority Rakhine, the Rohingya have long experienced persecution.
The army launched an operation in Rakhine last month after deadly attacks on police stations, which it blamed on militants. Myanmar's military has repeatedly denied targeting civilians but witnesses, refugees and journalists have contested this.