WASHINGTON — After days of anti-American violence across the Muslim world, the White House is girding itself for an extended period of turmoil that will test the security of American diplomatic missions and President Obama’s ability to shape the forces of change in the Middle East.

Although the tumult subsided Saturday, senior administration officials said they had concluded that the sometimes violent protests in Muslim countries may presage a period of sustained instability with unpredictable diplomatic and political consequences. While pressing Arab leaders to tamp down the unrest, Mr. Obama’s advisers say they may have to consider whether to scale back diplomatic activities in the region.

The upheaval over an anti-Islam video has suddenly become Mr. Obama’s most serious foreign policy crisis of the election season, and a range of analysts say it presents questions about central tenets of his Middle East policy: Did he do enough during the Arab Spring to help the transition to democracy from autocracy? Has he drawn a hard enough line against Islamic extremists? Did his administration fail to address security concerns?

These questions come at an inopportune time domestically as Mr. Obama enters the fall campaign with a small lead in polls. His policies escaped serious scrutiny in the initial days after the attack that killed four Americans in Libya last week, in part because of the furor over a statement by Mitt Romney accusing the president of sympathizing with the attackers. White House officials said they recognized that if not for Mr. Romney’s statement, they would have been the ones on the defensive.