They issued a statement Wednesday urging the government to explain its policies on handling the ethnic conflict in Rakhine state, where officials say about 90 people were killed last month and more than 30,000 made homeless.
They stressed that the concerns of both groups—Rakhine Buddhists and Rohingya Muslims—should be addressed.
In earlier violence in June, about the same number of people were killed and 75,000 were made homeless.
Suu Kyi has emphasized the necessity of restoring the rule of law and dealing with the root causes of the tensions.
Many of her foreign supporters have been disappointed that she has not taken a stand condemning discrimination toward the Rohingya, who have suffered most of the casualties and losses in the latest violence.
The statement also said the government should be clear about how it intends to apply a 1982 law that deals with the rules for citizenship for those who consider themselves Rohingya. Most of the U.N.-estimated 800,000 Rohingya in Myanmar are stateless.
The statement did not mention neighboring Bangladesh by name, but suggested that it contributed to the problem. Many in Myanmar regard the Rohingya as being mostly illegal immigrants from Bangladesh, though the number in that category is hotly debated.
"Both governments that share common boundaries should respect and take responsibility for border security and immigration matters," it said. "It is imperative that both countries systematically prevent border crossings and ensure border security."
Bangladesh also refuses to consider the Rohingya its citizens, and blocks those trying to enter from Myanmar, though it houses many in refugee camps.