AMBASSADOR J. Christopher Stevens was the sort of U.S. diplomat who makes a difference. Fluent in Arabic, he roamed the streets of Tripoli and Benghazi, listening more than talking. When he did speak, he pushed hard for Libyans to embrace liberal democracy — and for the United States to stand behind those who took up that cause.

In the wake of his tragic death, the biggest threat to U.S. interests in the Middle East is not that more embassies will be assaulted and more envoys killed. It is that, out of fear of that prospect or anger at what occurred, the United States will not follow Mr. Stevens’s example.

Misunderstanding of the anti-American demonstrations, which have continued to spread in the Arab world, could easily lead to poor decisions in Washington. The protests should be seen not as a popular uprising against an obscene but obscure film, or as a rejection of the United States, but as part of a struggle for power in Egypt, Libya, Tunisia and other countries where the old autocratic political order has been demolished.

Militant Islamic movements, which in several of those countries have been losing ground to more moderate Muslim and liberal forces, seize on pretexts such as the anti-Muslim film to mobilize against their political enemies, exploiting widespread misconceptions among Arabs about the United States and its policy toward the Islamic world. By design, they force more moderate Islamists, such as Egyptian President Mohamed Morsi and his Muslim Brotherhood, to balance their desire for constructive relations with Washington against the competition with militants for popular support. That squeeze helps to explain, if not to excuse, Mr. Morsi’s slow and ambiguous response to the initial protests in Cairo.

The intelligent U.S. response to these circumstances is not to cut off aid to Egypt — as some in Congress demand — or to pressure Mr. Morsi for difficult but largely symbolic statements or acts. It is to undermine the extremists’ strategy by refuting the attempts to portray U.S. society and government as anti-Muslim; by pragmatically working with governments to renew economic growth and combat violent jihadists; and by continuing to support the liberal political movements that, as much as the Islamists, are fighting to win broad public support.

President Obama’s response to last week’s crisis largely followed that path. The administration repeatedly denounced the offending film while defending freedom of speech. Mr. Obama dispatched Marines to the region to protect embassies and quietly pushed Mr. Morsi to adopt appropriate security measures while making it clear that the United States will continue to support economic development in Egypt.

The administration’s greatest failing during the Arab revolutions has been not displays of weakness, as Mitt Romney has charged, but excessive caution. It has been too slow to support legitimate movements for change, to back moderates over extremists and to take risks. It has consistently underestimated the power of the United States to positively influence events from Libya to Syria. The future of the Arab world is up for grabs; the United States should be doing everything it can to tilt it toward freedom. That means embracing the example of Christopher Stevens.