Stories and images of migrants pouring into Europe are inspiring thousands more, from Iraq to Nigeria, to rush out on their own risky journeys, posing a burgeoning problem for policy makers who are focused mainly on easing the plight of Syrian refugees.

Inspired by phone calls and Facebook posts from friends hiking through the Balkans, crossing into Germany or simply touching dry land in Greece, people from countries long plagued by war and instability say they are seizing a pivotal moment.

“This is a golden opportunity,” said Osama Ahmed, 27 years old, who lined up Sunday at Baghdad International Airport, heading for Greece via Turkey with five friends. “It’s totally nonsense to stay in Iraq when there is a chance to go.”

The prospect of a secondary wave comes as the European Union tries to hammer out a common response to the crisis already on its shores. Germany, which has taken in the most asylum seekers, wants other EU countries to absorb more. France and the U.K. announced Monday they would do so. But other governments have resisted, fearing a political backlash.

Syrians still make up the bulk of the outflow. In Turkey, which hosts almost two million Syrian refugees, officials spoke of a rush for the border, sparked by Berlin’s decision last month to waive EU rules, on humanitarian grounds, and allow Syrian refugees to stay however they arrived in Germany.