SANAA, Yemen — Chanting “death to America” and “death to Israel,” hundreds of protesters angered by an anti-Islam film stormed the U.S. Embassy compound in Yemen’s capital and burned the American flag on Thursday, the latest in a series of attacks on American diplomatic missions in the Middle East.

The string of assaults this week, in Yemen, Egypt and the storming of a U.S. consulate in Libya that killed four Americans, point to an increased boldness among Islamists who have become more powerful since last year’s wave of revolts toppled authoritarian leaders.

The anger over the movie denigrating Islam’s Prophet Muhammad has also put the region’s new leaders — some of whom are themselves Islamists — in a difficult corner, between a base demanding a free hand to respond to the insult and U.S. pressure to crack down. In the past, protests have broken out over perceived insults to Islam from the West, but in Arab countries they never escalated to the degree of breaching embassies, suggesting now hard-liners feel they can act with impunity.

Yemen’s president, Abed Rabbo Mansour Hadi, quickly apologized to the U.S. for the embassy attack and vowed track down the culprits, just as Libya’s president did. Egypt’s Islamist President Mohammad Morsi, who had been slow to speak out on Tuesday’s assault on the embassy in Cairo, promised Thursday that his government would not allow attacks on diplomatic missions.

U.S. officials suspect the Libya assault may have been a planned terror operation rather than a spontaneous mob assault. While protesters in other countries were unarmed, a crowd bristling with machine guns and rocket-propelled grenades overwhelmed the consulate in Benghazi late Tuesday, killing the ambassador and three other Americans.