They also want a requirement that the US and Australia pay families compensation if their loved ones die during strikes.
“Both Trump and Turnbull should commit to providing compensation for wrongful civilian deaths and injuries as required by international law, and appropriate “condolence” or ex gratia payments for other civilian harm,” Human Rights Watch’s Iraq researcher Belkis Wille said in a statement.
Mr Turnbull is in New York and has met President Trump over commemorations for the 75th anniversary of the Battle of the Coral Sea.
Ms Wille says it’s a good time for Mr Turnbull to raise the issue of changes to the military targeting process in the operations against ISIS, given it’s been 1000 days since the campaigns in Syria and Iraq.
Pointing to reports the US has removed the need for a cell in Baghdad to approve strikes beforehand, Ms Willkie said that could mean less reliance on information and targeting recommendations.
“Turnbull and other coalition leaders should urge Trump to roll back the change,” Ms Wille said.
“This is particularly important given the high risk to civilians in densely populated western Mosul, the current focus of military action."
There should also be verification of the presence and location of combatants as well as civilians, she said.
“Surveillance, intelligence and reconnaissance efforts should be dedicated to conducting ‘pattern of life’ analyses, locating and tracking civilians moving in and out of potential and future target areas in advance of operations to reduce the risk of civilian casualties.”
Ms Wille said the announcement by the Australian Defence Force to publish reports on strikes was a step in the right direction.