WASHINGTON  President Obama ordered his advisers last August to produce a secret report on unrest in the Arab world, which concluded that without sweeping political changes, countries from Bahrain to Yemen were ripe for popular revolt, administration officials said Wednesday.

Mr. Obama’s order, known as a Presidential Study Directive, identified likely flashpoints, most notably Egypt, and solicited proposals for how the administration could push for political change in countries with autocratic rulers who are also valuable allies of the United States, these officials said.

The 18-page classified report, they said, grapples with a problem that has bedeviled the White House’s approach toward Egypt and other countries in recent days: how to balance American strategic interests and the desire to avert broader instability against the democratic demands of the protesters.

Administration officials did not say how the report related to intelligence analysis of the Middle East, which the director of the Central Intelligence Agency, Leon E. Panetta, acknowledged in testimony before Congress, needed to better identify “triggers” for uprisings in countries like Egypt.