HONG KONG — Daw Aung San Suu Kyi, the de facto leader of Myanmar and a Nobel Peace Prize laureate who once embodied her country’s fight for democracy, came under increased pressure on Monday to denounce a military operation that has caused thousands of Muslim refugees to flee across the border to Bangladesh.

As protests erupted across the region and a fellow peace prize laureate took to Twitter to confront Ms. Aung San Suu Kyi, some wondered whether the Nobel Committee, which conferred the honor on her in 1991, would publicly criticize her or could even revoke the prize.

Demonstrations against the targeting of the Rohingya ethnic group, a persecuted Muslim minority, took place on Monday outside Australia’s Parliament in Canberra. In Jakarta, Indonesia, protesters burned photos of Ms. Aung San Suu Kyi and lobbed a gasoline bomb at the Myanmar Embassy.