"We discussed the situation in Rakhine state at considerable length today", Turnbull said at a joint press conference with Singapore Prime Minister Lee Hsien Loong that marked the end of the Asean-Australia Special Summit.
Neither Suu Kyi nor Turnbull made public remarks before their meeting, but the Australian leader said on Sunday that Suu Kyi spoke "at considerable length" during the ASEAN meeting about Rakhine State, appealing to her Southeast Asian neighbors for humanitarian help.
Myanmar's State Counsellor was due to give a speech and take questions from the audience at a Lowy Institute event on Tuesday.
Among the atrocities, villages were burned, women raped and babies murdered.
Despite facing widespread worldwide condemnation, Suu Kyi was welcomed to Parliament House in Canberra today by a 19-gun salute.
Suu Kyi has been criticised by large swathes of the global community for failing to protect the Rohingya - who are considered by the majority of Myanmar citizens as illegal "Bengali" immigrants and denied citizenship by the government - and for refusing to condemn the military amid mounting evidence that it has indiscriminately killed, raped and tortured innocent civilians, and burnt down entire villages.
Pressure has been building on Ms Suu Kyi over the plight of Rohingya Muslims in the north of her country, as Mr Turnbull reveals the Nobel Peace Prize victor turned to leaders from ASEAN's nine other member countries for humanitarian help.
Bangladesh and Myanmar have agreed to send some of the refugees back across the border, but so far only around 8,000 Rohingya have applied to be sent home.
It won't be much of a heroes' welcome when Myanmar's de facto leader Aung San Suu Kyi returns to Canberra for the first time in five years.
Since coming to power in 2016, Suu Kyi, who won the 1991 Nobel Peace Prize for her struggle for democracy in Myanmar, has faced growing criticism for failing to condemn or stop military attacks on her country's minority Rohingya Muslims.
Opposition Leader Bill Shorten also raised the plight of the Rohingya Muslims with Ms Suu Kyi at a meeting in Canberra with shadow foreign minister Penny Wong.
Ms Suu Kyi has not denounced military action or addressed genocide claims.
In response to questions posed by Reuters about the lawyers' move, Suu Kyi spokesman Zaw Htay said earlier in the day such "pressure" was unhelpful in solving the conflict in Rakhine, which he called "the Bengali problem" - using a term to describe the Rohingya that suggests they are interlopers from Bangladesh. She has not spoken publicly on the subject since.
The United Nations has dubbed the violence a text book case of "ethnic cleansing".
Myanmar staunchly denies that its security forces have targeted civilians in Rakhine state. Australia provides English-language lessons and training courses to Myanmar officers to "promote professionalism and adherence to worldwide laws" according to the defence department.