Top U.S. arms makers are straining to meet surging demand for precision missiles and other weapons being used in the U.S.-led fight against Islamic State and other conflicts in the Middle East, according to senior U.S. officials and industry executives.

Global demand for U.S.-made missiles and so-called smart bombs has grown steadily since their use in the first Gulf War. But the United States and a host of allies are now rushing to ensure a stable supply of such weapons for what is expected to be a long fight against Islamic State, whose rise has fueled conflict in Syria and across a swathe of the Middle East.

U.S. officials say arms makers have added shifts and hired workers, but they are bumping up against capacity constraints and may need to expand plants or even open new ones to keep weapons flowing. That could create further log-jams at a time when U.S. allies are voicing growing concern that Washington’s processing of arms sales orders is too slow. […]