WASHINGTON—President Barack Obama asked Congress for new powers to wage military operations against the Islamic State militant group, kicking off a renewed national debate over the scope of wartime powers that should be afforded to the commander-in-chief.

American warplanes have pounded Islamic State targets for six months, but Mr. Obama on Wednesday said the proposed resolution authorizing military force is important not only for the U.S. strategy against the group, but also to the cohesion of an international coalition,...